helpersssssssssssssss

The probability assignment is Pr(03) ≈ 0.1133, and Pr(04) = Pr(05) ≈ 0.1133 each.

(a) Given that events 03, 04, and 05 have the same probability, let's denote their probability as p. We know that the sum of probabilities in the sample space S must equal 1. So, we have:

Pr(0) + Pr(1) + Pr(2) + Pr(03) + Pr(04) + Pr(05) = 0.01 + 0.01 + 0.03 + p + p + p = 1

Combining and solving for p:

0.05 + 3p = 1

3p = 0.95

p = 0.95 / 3 ≈ 0.3167

So, the probability assignment is Pr(03) = Pr(04) = Pr(05) ≈ 0.3167.

(b) Given that Pr(S) = 0.34, and Pr(03) has the same probability as 04 and 05 combined, we can write:

Pr(03) + Pr(04) + Pr(05) = 0.34

Let's denote the probability of 03 as q and the combined probability of 04 and 05 as 2q. So:

q + 2q = 0.34

3q = 0.34

q ≈ 0.1133

Therefore, the probability assignment is Pr(03) ≈ 0.1133, and Pr(04) = Pr(05) ≈ 0.1133 each.

To learn more about probability, click here:

brainly.com/question/30034780

#SPJ11

The Addition Rule says that P(A or B) = P(A) + P(B) when:

b. The events must be disjoint.

According to the Addition Rule, P(A or B) = P(A) + P(B) is true when the events must be disjoint.
Disjoint events, also known as mutually exclusive events, are events that cannot occur simultaneously.

In other words, if one event occurs, the other event cannot occur at the same time.

Since there's no overlap between these events, we can simply add their individual probabilities to find the probability of either event A or event B occurring.

Option b. The events must be disjoint is correct.

For similar question on Addition.

https://brainly.com/question/29170774

#SPJ11

According to the ANOVA, the variance between groups to the variance within groups to determine if the group means are significantly different from each other.

The sum of squares for each group is the sum of the squared differences between each observation in the group and the group mean. The sum of squares for the total is the sum of the squared differences between each observation and the overall mean.

Once we have the sum of squares for each group and the sum of squares for the total, we can calculate the degrees of freedom and the mean squares for each source of variation.

Using the given data, we can calculate the sum of squares for each group, the sum of squares for the total, and the mean squares for each source of variation. Then, we can calculate the F-statistic and compare it to the critical value for a = .05 to determine if there is a significant difference between the groups.

Hence the correct group is 3.

To know more about ANOVA here

https://brainly.com/question/23638404

#SPJ4

[tex]\sqrt{x+2}=x-4\implies (\sqrt{x+2})^2=(x-4)^2\implies x+2=x^2-8x+16 \\\\\\ 0=x^2-9x+14\implies 0=(x-7)(x-2)\implies x= \begin{cases} 7 ~~ \textit{\LARGE \checkmark}\\ 2 ~~ \bigotimes \end{cases}[/tex]

why is x = 2 not good?  well, plug it in, making the assumption that we're using only the positive root, 2 ≠ -2.

When the sample size is too small, it may be necessary to use alternative statistical tests or to collect a larger sample to ensure the accuracy and reliability of the results obtained.

The success-failure condition is a requirement for using certain statistical tests, such as the z-test and chi-square test. This condition requires that the sample size is large enough such that both the number of successes and the number of failures in the sample are at least 10.

The reason for this requirement is that statistical tests rely on the assumption of a normal distribution, which is not accurate when the sample size is too small. When the sample size is small, the distribution of the data may be skewed or have a high level of variability, which can lead to inaccurate or unreliable results.

When the success-failure condition is not met, it may be necessary to use alternative statistical tests or to collect a larger sample.

To know more about sample size here

https://brainly.com/question/30885988

#SPJ4

Yes, the distributor has a right to complain to the water bottling company because a 1-gallon bottle containing exactly 1-gallon of water lies outside the 95% confidence interval.

The 95% confidence interval is a statistical measure that provides a range of values within which a true population parameter is likely to fall with 95% confidence. If a 1-gallon bottle containing exactly 1-gallon of water lies outside this confidence interval, it means that the actual quantity of water in the bottle is either significantly higher or significantly lower than the expected amount. This indicates a potential issue with the accuracy or consistency of the water bottling process.

The fact that the measured quantity of water falls outside the 95% confidence interval suggests that there may be inconsistencies or errors in the water bottling process, resulting in variations in the amount of water being filled into the bottles. This can be a valid reason for the distributor to complain to the water bottling company, as it indicates a lack of quality control and adherence to standards in the production process.

Therefore, based on the results indicating that a 1-gallon bottle containing exactly 1-gallon of water lies outside the 95% confidence interval, the distributor has a right to complain to the water bottling company about the potential inconsistency in the quantity of water in the bottles.

To learn more about confidence interval here:

brainly.com/question/24131141#

#SPJ11

If a car costs $5,700.00 with a tax rate of 8% and you make a down payment of 15% and trade in $650, the total amount of the loan will be $4,582.60.

A down payment is an initial or advance payment made to reduce the loanable amount or the total cost of an item resulting from a purchase transaction.

Down payments are stated as percentages of the total amount or cost of an item.

After reducing the loanable amount by the down payment, the difference is the loan due.

The cost of a car = $5,700.00

Tax rate = 8% = $456.00 ($5,700.00 x 8%)

The total cost plus sales tax = $6,156.00 ($5,700.00 + $456.00)

Down payment = 15% = $923.40 ($6,156.00 x 15%)

Trade-in value = $650.00

Total loan amount = $4,582.60 ($6,156.00 - $923.40 - $650.00)

Learn more about down payments at https://brainly.com/question/15623552.

#SPJ1

the likelihood of the arbitrary(random) number generator producing a 6 is 1/10 or 0.1. 

A uniform distribution may be a likelihood distribution in which all conceivable results are similarly likely.

Within the case of an arbitrary number generator that creates numbers irregular numbers between and 9 comprehensive taking after a uniform distribution, each number has the same likelihood of being produced, which is 1/10 (or 0.1).

This implies that the likelihood of producing any particular number, such as 6, is additionally 1/10 (or 0.1).

The concept of a uniform distribution is imperative in insights and likelihood hypothesis since it permits us to demonstrate circumstances where we have no reason to accept that any specific result is more likely than any other result.

For illustration, in case we were rolling a reasonable six-sided pass on, we would anticipate each number to be similarly likely to come up.

In rundown, the uniform distribution could be a simple but imperative concept in the likelihood hypothesis, and it is regularly utilized to demonstrate circumstances where all results are similarly likely.

Within the case of an arbitrary number generator that creates numbers arbitrary numbers between and 9 comprehensive taking after a uniform distribution, each number has the same likelihood of being produced, which is 1/10 (or 0.1). 

To know more about uniform distribution refer to this :

https://brainly.com/question/22209943

#SPJ4

The length of the square is increasing at the rate of 1/10 m/s when 25 square meters is the area of the square .

What is the area of square?

Area of a square is side × side.

We know that A = x² where x is side of the square.

Taking the derivative of both sides with respect to time t,

dA/dt = 2x(dx/dt) where dx/dt is the rate of increasing of the length of the square.

It is given that dA/dt = 1 m/s when A = 25 m².

Putting these values into the above equation,

1 = 2x(dx/dt) When A = 25, x = √(25) = 5.

Putting this value into the equation above,

1 = 2(5)(dx/dt)

Simplifying this equation,

dx/dt = 1/10 m/s

Therefore, the length of the square is increasing at the rate of 1/10 m/s when 25 square meters is the area of the square .

Learn more about area of a square here,

https://brainly.com/question/25092270

#SPJ1

Answer:

the answer is B. 1/y^3.

Step-by-step explanation:

The expression y^-3 can be simplified as follows:

y^-3 = 1/y^3

Therefore, the answer is 2. 1/y^3.

Answer: The simplified expression for y ^-3 is 1/y^3.

Step-by-step explanation: To understand this solution, it is important to understand the concept of negative exponents. When a number or variable is raised to a negative exponent, it means that the reciprocal of that number or variable is taken to the positive exponent.

In this case, y ^-3 can be rewritten as 1/y^3. This is because y^-3 is the same as 1/y^3. Therefore, the answer to this question is option (2) 1/y^3.

Answer:

Acceleration rate = (3 km/hr)/sec =

(3 km/3,600 sec)/sec =

(1 km/1,200 sec)/sec

Initial velocity= 20 km/hr =

20 km/3,600 sec = 1 km/180 sec

(1/180) + (1/1,200)(30) = 11/360 km/sec

= 110 km/3,600 sec = 110 km/h

f(x) = 4x^2 -7

f(2) = 4*2^2 -7

= 16-7

=9

With a 30% discount off the cost of the backpack while Dalia pays $33.39, the original price of the backpack was $47.70.

The discount represents the amount or percentage by which the original price of an item is reduced before being sold.

Given the discounted price and the discount rate, the original price can be determined as follows:

The discount offered for the backpack = 30%

The discounted price = $33.39

Discount factor = 0.7 (1 - 0.3)

Original price = $47.70 ($33.39 ÷ 0.7)

Learn more about discounts at https://brainly.com/question/28176129.

#SPJ1

The number of bins of bottles collected by Shelby = 38

Let us assume that x represents the bins of glass bottles collected by Pam and y represents the bins of glass bottles collected by Shelby.

Here, x = 7 1/2

We write this improper fration as proper fraction.

7 1/2 = 15/2

Shelby collected 5 1/8 times as many bins as Pam.

First we write 5 1/8 improper fration as proper fraction.

5 1/8 = 41/8

From above statement we get an expression,

y = ( 5 1/8) × x

y = (41/8) × x

y = 41/8 × 15/2

y = 38.43

y ≈ 38

Therefore, Shelby collected approximately 38 bins of bottles.

Learn more about an expression here:

https://brainly.com/question/1859113

#SPJ1

A random variable has a normal distribution with a standard deviation (0) = 3.8. If the probability is 0.9713 that the random variable will take on a value less than 85.6, then 0.0352 is the probability that it will take on a value between 76 and 79.

To solve this problem, we need to use the properties of the normal distribution and standard deviation.
First, we can use a standard normal distribution table (also known as a z-table) to find the corresponding z-score for the probability of 0.9713. This z-score is approximately 2.07.
Next, we need to find the z-scores for the values 76 and 79. To do this, we use the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean (which we don't know but can assume to be close to 85.6), and σ is the standard deviation of 3.8.
For x = 76, we have z = (76 - 85.6) / 3.8 = -2.53. For x = 79, we have z = (79 - 85.6) / 3.8 = -1.74.
Now, we can use the z-table again to find the probabilities associated with these z-scores. The probability of getting a z-score less than -2.53 is approximately 0.0057, and the probability of getting a z-score less than -1.74 is approximately 0.0409.
Finally, we can find the probability of the random variable taking on a value between 76 and 79 by subtracting the probability of getting a z-score less than -2.53 from the probability of getting a z-score less than -1.74. This gives us:
P(76 < X < 79) = P(Z < -1.74) - P(Z < -2.53)
≈ 0.0409 - 0.0057
≈ 0.0352
Therefore, the probability that the random variable will take on a value between 76 and 79 is approximately 0.0352.

To learn more about probability, refer:-

https://brainly.com/question/30034780

#SPJ11

The upper left corner with an x-value of 10 and a y-value of 20 to the given scatterplot would likely decrease the value of the correlation coefficient, r.

The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative correlation) to 1 (perfect positive correlation), with 0 indicating no correlation. In a scatterplot, points that are closer to forming a straight line indicate a stronger linear relationship, while points that are more scattered indicate a weaker linear relationship.

In the given scatterplot, adding a point in the upper left corner with an x-value of 10 and a y-value of 20 would likely introduce an outlier that deviates from the overall pattern of the data. This outlier would be located far away from the other points, potentially causing the scatterplot to become more scattered and less linear. As a result, the linear relationship between the two variables, as measured by the correlation coefficient, r, would likely decrease. This is because the outlier would have a disproportionate influence on the calculation of the correlation coefficient, pulling it closer to 0 or even changing the direction of the correlation, if the outlier introduces a different pattern to the data.

Therefore, adding a point in the upper left corner with an x-value of 10 and a y-value of 20 to the given scatterplot would likely decrease the value of the correlation coefficient, r.

To learn more about correlation coefficient here:

brainly.com/question/15577278#

#SPJ11

The standard form of the arithmetic sequence -18, -10, -2, 6, ... is: an = 8n - 26.

To write the arithmetic sequence -18, -10, -2, 6, ... in standard form, we first need to identify the common difference between the terms. To do this, we can subtract each term from the one that comes after it:

-10 - (-18) = 8
-2 - (-10) = 8
6 - (-2) = 8

Since each difference is 8, we know that this is an arithmetic sequence with a common difference of 8.

To write the sequence in standard form, we use the formula:

an = a1 + (n-1)d

where an is the nth term in the sequence, a1 is the first term, n is the term number, and d is the common difference.

In this case, a1 = -18 and d = 8.

So, to find the nth term, we use:

an = -18 + (n-1)8

Expanding the brackets gives:

an = -18 + 8n - 8

Simplifying:

an = 8n - 26

Know more about arithmetic sequence here:

https://brainly.com/question/15412619

#SPJ11

The value of k is 0.52, and the answer is (C).

We can use the cumulative distribution function to calculate the probabilities of the random variable X taking on certain values.

From the given values, we know that:

F(12) = 0.34

F(19) = 0.37

F(25) = 0.43

F(31) = 0.46

F(37) = k

F(43) = 0.55

F(49) = 0.6

To find the value of k, we can use the property that the cumulative distribution function is non-decreasing. Therefore, we have:

Pr[19 < X < 37] = F(37) - F(19) = k - 0.37

Since Pr[19 < X < 37] = 0.15, we can set up the equation:

0.15 = k - 0.37

Solving for k, we get:

k = 0.52

Therefore, the value of k is 0.52, and the answer is (C).

learn more about probability,

https://brainly.com/question/13604758

#SPJ11

Augmented matrix of the equations -8x-4y = -4 and -6x+8y = -3 is

[tex]\left[\begin{array}{cc|c}-8&-4&-4\\-6&8&-3\end{array}\right][/tex]

and the final reduced row echelon form [tex]=\left[\begin{array}{cc|c}1&0&\frac{1}{2}\\0&1&0\end{array}\right][/tex]

Solutions are x = 1/2 and y = 0.

The simultaneous equations are,

-8x - 4y = -4

-6x+8y = -3

The Augmented matrix will be =

[tex]\left[\begin{array}{cc|c}-8&-4&-4\\-6&8&-3\end{array}\right][/tex]

Subtracting (3/4) of the first row to the second row we get,

[tex]\left[\begin{array}{cc|c}-8&-4&-4\\0&11&0\end{array}\right][/tex]

Multiplying (1/11) with second row we get,

[tex]\left[\begin{array}{cc|c}-8&-4&-4\\0&1&0\end{array}\right][/tex]

Multiplying (-1/8) with first row we get,

[tex]\left[\begin{array}{cc|c}1&\frac{1}{2}&\frac{1}{2}\\0&1&0\end{array}\right][/tex]

Subtracting (1/2) of second row with first row we get,

[tex]\left[\begin{array}{cc|c}1&0&\frac{1}{2}\\0&1&0\end{array}\right][/tex]

This is the reduced row echelon form.

So the solutions of the equations are, x = 1/2 and y = 0.

To know more about Augmented Matrix here

https://brainly.com/question/29028693

#SPJ4

The number of no-shows for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution.

No-shows Probability

0 0.30

1 0.20

2 0.20

3 X

4 0.15

The following

Expected value = (0)(0.30) + (1)(0.20) + (2)(0.20) + (3)(X) + (4)(0.15)

= 0 + 0.20 + 0.40 + 0.15(4) + 3X

= 1.20 + 3X

Since the sum of the probabilities must equal 1, we have

0.30 + 0.20 + 0.20 + X + 0.15 = 1

X = 0.15

Therefore, the expected value of the number of no-shows is

Expected value = 1.20 + 3(0.15) = 1.65

To find the variance, we can use the formula

Variance =[tex](0 - 1.65)^2(0.30) + (1 - 1.65)^2(0.20) + (2 - 1.65)^2(0.20) + (3 - 1.65)^2(0.15) + (4 - 1.65)^2(0.15)[/tex]= 0.5625

Therefore, the variance is 0.5625, which means the standard deviation is the square root of the variance.

Standard deviation = [tex]\sqrt{0.5625}[/tex] = 0.75

Hence, the correct option is A 1.65 customers.

Hence, the correct option is E 0 customers.

We have already found the variance to be 0.5625.

Hence, the correct option is C 0.15.

We have already found the expected value to be 1.65.

Hence, the correct option is D 1.424.

To know more about probability distribution here

https://brainly.com/question/13993948

#SPJ4

This is our second approximation, x2 = -1/2. Our third approximation is x3 = 7/4. This can be answered by the concept of differentiation.

To use Newton's method to approximate a root of the equation z² + 2 = 0, we start with an initial approximation of i = -1.

The formula for Newton's method is:

x_(n+1) = x_n - f(x_n)/f'(x_n)

where x_n is the nth approximation, f(x_n) is the function evaluated at x_n, and f'(x_n) is the derivative of the function evaluated at x_n.

For our equation, f(z) = z² + 2, so f'(z) = 2z.

Using the initial approximation of i = -1, we have:

x_1 = -1 - (-1² + 2)/(2(-1)) = -1 - (-1)/(-2) = -1 + 1/2 = -1/2

This is our second approximation, x2 = -1/2.

To find the third approximation, we use x_2 as our new initial approximation:

x_3 = -1/2 - ((-1/2)² + 2)/(2(-1/2)) = -1/2 - (1/4 + 2)/(-1) = -1/2 + 9/4 = 7/4

Therefore, our third approximation is x3 = 7/4.

To learn more about differentiation here:

brainly.com/question/31495179#

#SPJ11

The probability of a Type I error is equal to the significance level, which is given as a=0.05 so the probability of a Type I error is 0.05.

The probability of a Type I error is the probability of rejecting a null hypothesis when it is actually true. In other words, it is the probability of concluding that there is a significant effect or difference when in reality there is none.

This probability is denoted by alpha (α) and is usually set at a predetermined level, such as 0.05 or 0.01. In this question, the sample size is 120, and the probability of a Type II error (B) is given as 0.68. To find the probability of a Type I error, we need to subtract the probability of a Type II error from 1 and divide the result by 2. Therefore, the probability of a Type I error is (1 - 0.68) / 2 = 0.16.

Learn more about the probability at

https://brainly.com/question/30034780

#SPJ4

A. An example of a power series with a radius of convergence of 0 is Σ n=0 (n!)xⁿ. This series converges only at its center (x=0) but nowhere else.

B. The radius of convergence of the power series Σ n=0 (Cn + Dn) xⁿ is 2. The radii of convergence of the individual power series do not directly determine the radius of convergence of their sum.

C. No, it is not possible for the interval of convergence of a power series to be (0,∞). A power series converges within a specific interval, called the interval of convergence, which is always symmetric about its center. The interval of convergence will always have finite bounds, so it cannot be (0,∞).

To know more about power series click on below link:

https://brainly.com/question/29896893#

#SPJ11

This is the required probability density function for Z.

Since the task is complete only when the computation at both worker nodes is complete, the total time for completion of the task is the maximum of X and Y.

Therefore, we have:

Z = max(X,Y)

The CDF of Z can be written as:

[tex]F_Z(z)[/tex] = P(Z <= z) = P(max(X,Y) <= z)

Since X and Y are independent, we have:

P(max(X,Y) <= z) = P(X <= z, Y <= z)

Using the properties of exponential distribution, we have:

P(X <= z, Y <= z) = P(X <= z) * P(Y <= z)

[tex]= (1 - e^{-l1 * z}) * (1 - e^{-l2 * z})[/tex]

Therefore, the CDF of Z is:

[tex]F_Z(z) = (1 - e^(-l1 * z)) * (1 - e^(-l2 * z))[/tex]

To find the PDF of Z, we differentiate the CDF with respect to z:

[tex]f_Z(z) = d/dz F_Z(z)[/tex]

[tex]= l1 * e^{-l1 * z} * (1 - e^{-l2 * z}) + l2 * e^{-l2 * z} * (1 - e^{-l1 * z}) \\[/tex]

Therefore, the PDF of Z is:

[tex]f_Z(z) = l1 * e^{-l1 * z} * (1 - e^{-l2 * z}) + l2 * e^{-l2 * z} * (1 - e^{-l1 * z})[/tex]

For similar question on probability.

https://brainly.com/question/9448926

#SPJ11

A simple random sample of housing prices is taken from each region.

[tex]H0: \mu_s = \mu_N[/tex]

Degree of Freedom [tex]df = n_N + n_s - 2[/tex].

Point estimate for the southern part of the country x_s and the northern part to the country x_N.

The test statistic is:

[tex]t = (x_N - x_s) / (\sqrt{((s_N^2/n_N) + (s_s^2/n_s))})[/tex]

The problem does not provide the sample data for the two regions, so we cannot determine the sample size, degrees of freedom, or point estimates for the mean housing prices.

The sample data has been collected and proceed to conduct a hypothesis test to determine if there is evidence to support the agent's claim.

Let μ_s be the population mean home price in the southern part of the county and μ_N be the population mean home price in the northern part of the county.

The null hypothesis is that the mean home prices in the two regions are equal:

[tex]H0: \mu_s = \mu_N[/tex]

The alternative hypothesis is that the mean home price in the northern part of the county is higher than the mean home price in the southern part of the county:

[tex]Ha: \mu_N > \mu_s[/tex]

A two-sample t-test to compare the means of the two independent samples.

The test statistic is:

[tex]t = (x_N - x_s) / (\sqrt{((s_N^2/n_N) + (s_s^2/n_s))})[/tex]

where x_N and x_s are the sample means, s_N and s_s are the sample standard deviations, and n_N and n_s are the sample sizes for the northern and southern parts, respectively.

The null hypothesis, the test statistic follows a t-distribution with degrees of freedom given by:

[tex]df = n_N + n_s - 2[/tex]

The p-value for the test statistic and compare it to the significance level (α) to make a decision.

If the p-value is less than α, we reject the null hypothesis and conclude that there is evidence to support the agent's claim.

Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

The choice of significance level depends on the context and the consequences of making a Type I error (rejecting the null hypothesis when it is true) and a Type II error (failing to reject the null hypothesis when it is false). A common choice is α = 0.05.

For similar questions on random

https://brainly.com/question/30263705

#SPJ11

The limit as x approaches infinity for f(x) is 1/4.

To find the limit of f(x) as x approaches infinity, we need to examine the behavior of the function as x becomes very large.

First, we can divide the numerator and denominator of f(x) by [tex]x^3[/tex] to simplify the expression:

f(x) = [tex](1 - 2/x + 3/x^2 + 4/x^3) / (4 - 3/x + 2/x^2 - 1/x^3)[/tex]

As x becomes very large, all of the terms with powers of x in the denominator become very small, so we can ignore them. This gives us:

f(x) ≈ (1 + 0 + 0 + 0) / (4 + 0 + 0 + 0) = 1/4

Therefore, as x approaches infinity, the limit of f(x) is 1/4.

Learn more about infinity

https://brainly.com/question/17714945

#SPJ4

a. The unit price that yields maximum profit is $68 per unit.

b. The average cost (in dollars) per unit AC = $30.43

To find the maximum profit, we need to first write the profit function. Profit is defined as the revenue minus the total cost.

The revenue function is simply the product of the price and the quantity demanded, so we have:

R(x) = p(x) * x

R(x) = (106 - 0.5x) * x

R(x) = 106x - 0.5x^2

The total cost function is given as:

C(x) = 30x + 31.75

The profit function is therefore:

P(x) = R(x) - C(x)

P(x) = (106x - 0.5x^2) - (30x + 31.75)

P(x) = -0.5x^2 + 76x - 31.75

Now we need to find the value of x that maximizes profit.

To do this, we take the derivative of the profit function with respect to x and set it equal to zero:

P'(x) = -x + 76 = 0

x = 76

So the optimal number of units to produce and sell is 76.

To find the unit price that yields maximum profit, we plug x = 76 into the demand function:

p = 106 - 0.5x

p = 106 - 0.5(76)

p = $68 per unit

Therefore, the unit price that yields maximum profit is $68 per unit.

To find the average cost per unit when profit is maximized, we need to find the total cost when x = 76, and divide by the number of units:

C(76) = 30(76) + 31.75

C(76) = $2311.75

So the average cost per unit is:

AC = C(76) / 76

AC = $30.43 per unit (rounded to two decimal places).

For similar question on average cost.

https://brainly.com/question/31073216

#SPJ11

Using Bayes' Rule, we can find the probability of having the disease given a positive test: P(positive test) = P(positive test | D) * P(D) + P(positive test | not D) * P(not D)
P(D | positive test) = (0.99 * 0.01) / 0.0198 = 0.5

Using Bayes' theorem, we can calculate the probability of disease D given a positive test result, denoted as P(D|positive test). Bayes' theorem states:

P(D|positive test) = (P(positive test|D) * P(D)) / (P(positive test|D) * P(D) + P(positive test|not D) * P(not D))

Plugging in the given values:
P(D|positive test) = (0.99 * 0.01) / (0.99 * 0.01 + 0.01 * (1 - 0.01))

P(D|positive test) = (0.0099) / (0.0099 + 0.01 * 0.99)

P(D|positive test) = 0.0099 / (0.0099 + 0.0099)

P(D|positive test) = 0.0099 / 0.0198

P(D|positive test) = 0.5000

So, the probability of disease D given a positive test result is 0.5000.

Visit here to learn more about Probability:

brainly.com/question/13604758

#SPJ11

Based on the mentioned informations and provided values, the probability that the student answers at least 4 questions correctly is calculated to be 0.9511.

To solve this problem, we can use the binomial distribution. Let X be the number of questions the student answers correctly, then X is a binomial random variable with n = 19 and p = 1/3, since each question has 3 answer choices and the student is guessing randomly.

We want to find the probability that the student answers at least 4 questions correctly, which is the same as finding P(X >= 4). We can use the complement rule to calculate this probability:

P(X >= 4) = 1 - P(X < 4)

Now, we can use the cumulative distribution function (CDF) of the binomial distribution to calculate P(X < 4):

P(X < 4) = Σ P(X = k), k = 0 to 3

where P(X = k) is the probability of getting exactly k questions correct. This probability can be calculated using the binomial probability mass function:

P(X = k) = (n choose k) x p[tex].^{k}[/tex] x (1 - p)[tex].^{n-k}[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items. In our case, (n choose k) = 19 choose k.

Using this formula, we can calculate P(X < 4) as follows:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (19 choose 0) x (1/3)⁰ x (2/3)¹⁹

+ (19 choose 1) x (1/3)¹ x (2/3)¹⁸

+ (19 choose 2) x (1/3)² x (2/3)¹⁷

+ (19 choose 3) x (1/3)³ x (2/3)¹⁶

= 0.0489 (rounded to 4 decimal places)

Therefore, the probability that the student answers at least 4 questions correctly is:

P(X >= 4) = 1 - P(X < 4)

= 1 - 0.0489

= 0.9511 (rounded to 4 decimal places)

Learn more about Probability :

https://brainly.com/question/18882393

#SPJ4