What is the probability that a random sample of 17 pregnancies has a mean gestation period within 9 days of the mean?( length of pregnancies of a certain animal are approximately normally distributed with mean of 295 days and standard deviation of 15 days)
Answer:
0.9864
Step-by-step explanation:
The average sample mean is 295, and the standard deviation is:
σ = 15 / √17
σ = 3.64
The z-scores are:
z = (x − μ) / σ
z₁ = (-9) / 3.64
z₁ = -2.47
z₂ = (9) / 3.64
z₂ = 2.47
So the probability is:
P(-2.47 < Z < 2.47) = P(Z < 2.47) − P(Z < -2.47)
P(-2.47 < Z < 2.47) = 0.9932 − 0.0068
P(-2.47 < Z < 2.47) = 0.9864
Using the normal distribution and the central limit theorem, it is found that there is a 0.9864 = 98.64% probability that a random sample of 17 pregnancies has a mean gestation period within 9 days of the mean.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.For a sample of size n, by the Central Limit Theorem, the standard deviation is given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem:
Mean of 295 days, thus [tex]\mu = 295[/tex].Standard deviation of 15 days, thus [tex]\sigma = 15[/tex].Sample of 17 pregnancies, thus [tex]n = 17, s = \frac{15}{\sqrt{17}}[/tex].Gestation period within 9 days of the mean is between 286 and 304 days, and the probability is the p-value of Z when X = 304 subtracted by the p-value of Z when X = 286.
X = 304:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{304 - 295}{\frac{15}{\sqrt{17}}}[/tex]
[tex]Z = 2.47[/tex]
[tex]Z = 2.47[/tex] has a p-value of 0.9932
X = 286:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{286 - 295}{\frac{15}{\sqrt{17}}}[/tex]
[tex]Z = -2.47[/tex]
[tex]Z = -2.47[/tex] has a p-value of 0.0068
0.9932 - 0.0068 = 0.9864.
0.9864 = 98.64% probability that a random sample of 17 pregnancies has a mean gestation period within 9 days of the mean.
A similar problem is given at https://brainly.com/question/24663213
a/12 = 20 what is a?
Nathan earned $105,70 at his job when he worked for 7 hours. What was his
hourly wage, in dollars per hour?
Answer:
If it is $10,570 then the answer is 1510, but if you made a typo and meant 105,700, then the answer is 15100.
Answer:
Step-by-step explanation:
I divided 105.70 by 7 and got 15.1. So your answer is 15.10 cents I believe
Hope it helps :p
at 6:00 PM it’s 24°F at midnight the temperature was 636°F lower than Apple what will the temperature at midnight
Answer:
A)12 F.
Step-by-step explanation:
Which investment data is best modeled by an exponential function?
Answer:
Answer is C.
Step-by-step explanation:
Please like and mark brainliest, thanks :)
Exponential functions are functions that increases geometrically. The correct graph that model the investment is the Graph C
Exponential graphExponential functions are functions that increases geometrically. The standard exponential function is expressed as y = ab^x
The correct graph must represents a curve that increases steadily. From the given graph, the correct graph that model the investment is the Graph C
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Simplify the expression using the properties of operations.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is
Answer:
Step-by-step explanation:
5.23x+3.76-3.67x+6.39
x(5.23-3.67) +(3.76+6.39)
1.56x + 10.15
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
0 2:5 = 1:25
05:8= 20m
A researcher wants to test the relationship between SAT scores and high school GPA. What statistic should be used
Answer: Pearson correlation statistic
Step-by-step explanation:
The Pearson Correlation statistic is used to measure linear association. It simply measures the statistical relationship that exists between two variables that are continuous. Information about both the magnitude and the direction are being provided by the Pearson Correlation statistic.
Since both the SAT scores and the high school GPA has to do with numbers, we are going to use Pearson correlation statistic. Spearman correlation are used for ranking.
The value of the 8 in 89.945 is how many times rhe value of the 8 in 763.186
Answer:
1000x
Step-by-step explanation:
Let f(x) be defined for any positive integer x greater than 2 as the sum of all prime numbers less than x. For example, f(4)=2+3=5 and f(8)=2+3+5+7=17. What is the value of f(86)−f(82)?
(A) 3 (B) 4 (C) 47 (D) 59 (E) 83
The answer is not B pls remember this
Answer:
E
Step-by-step explanation:
RSM proves correct
The value of a given function is required.
So, the answer is (E)83.
The given function [tex]f(x)[/tex] is the sum of all prime numbers less than [tex]x[/tex].
The required function is [tex]f(86)-f(82)[/tex]
[tex]f(86)=2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83[/tex]
[tex]f(83)=2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79[/tex]
[tex]f(86)-f(83)=2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83-(2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79)=83[/tex]
All numbers become get subtracted except for 83.
So, the answer is (E)83.
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PLEASE HELP! Write the slope-intercept form of the equation of each line. Identify the slopes y-intercept
Answer:
3/2, 0, y=3/2x
-1/3, -2.5, y=-1/3x-2.5
1, 6, y=x+6
1/2, 2, y=1/2x+2
undefined, 0, x=-1
0, -4, y=-4
Step-by-step explanation:
hopefully this helps :)
dinners frequently add a 15% tip when charging a meal to a credit card. what is the price of the meal without the tip amount charged is $18.40? how much was the tip?
Answer:
Step-by-step explanation:
Let
'x' the price of the meal
15% of x or 0.15x is the tip
x + 0.15x = 20.70
1.15x = 20.70 divide both sides by 1.15
x = 20.70/1.15
x = $18
0.15*18 = $2.70
The price of the meal without the tip is $18.
The tip was $2.70.
A sofa regularly sells for $710. The sale price is $553.80. Find the percent decrease of the sale price from the regular price.
Given:
A sofa regularly sells for $710.
The sale price is $553.80.
To find:
The percent decrease of the sale price from the regular price.
Solution:
We have,
[tex]Decrease\%=\dfrac{\text{Regular price - Sale price}}{\text{Regular price}}\times 100[/tex]
[tex]Decrease\%=\dfrac{710-553.80}{710}\times 100[/tex]
[tex]Decrease\%=\dfrac{156.2}{710}\times 100[/tex]
[tex]Decrease\%=0.22 \times 100[/tex]
[tex]Decrease\%=22\%[/tex]
Therefore, the percent decrease of the sale price from the regular price is 22%.
A dolphin is 13 feet below sea level. A seagull is 3 feet above sea level.
. Write an integer for the position of each animal relative to sea level.
Can someone please help me with this I will mark Brainly to whoever does
Answer:
Try A
Step-by-step explanation:
I did it myself, and the first one I did, which was A, all had the same slope, so I think it is A.
Mario paid $30 to activate his cellular phone plus $50 per month. Type an equation:_
Answer:
50x + 30
Step-by-step explanation:
50 is the amount per month and x is how many months he's paying. If he's paying for 5 months then you replace x with 5 so on and so forth. the + 30 is the amount he paid to active his phone
Answer:
pa rompa pero no poden con mi pom pom con pom pom con pom pom
Step-by-step explanation:
The pair of polygons is similar. Find the value of x.
A. 2.5 in.
B. 5 in.
C. 35 in.
D. 40 in.
Answer: 40
60÷15=4
10×4=40
I hope this is good enough:
Select the correct answer.
Identify the end behavior and the zeros of function h.
h(x) = –13 – 9x2 + 41 +96
Based on these key features, which statement is true about the graph representing function h?
A. The graph is negative on the intervals (-00, -8) and (-4, 3).
B. The graph is positive on the intervals (-8, –4) and (3, 0).
C. The graph is positive on the intervals (-0, —8)and (-4, 3).
D. The graph is negative on the intervals (-3, 4) and (8,00).
Answer: C. The graph is positive on the intervals (-∞,-8) and (-4,3)
Step-by-step explanation: I guessed on my test and got it right. PLATO
Please help and tell me why you got that answer, will mark brainliest
Answer:
The answer is G.
Step-by-step explanation:
When comparing G with the other 3 options, ONLY G hasn't ran more than 6 miles; the rest all options show that he ran more miles in few minutes.
Mike and Krista rent a jet ski while on vacation. The rental cost is represented by the function c(h) = 50 + 20h, where h is the number of hours of use
and c(h) is the total cost for h hours of use. How much does the jet ski cost if they use it for 4 hours?
O $54
$80
. $130
$200
Answer:
130$
Step-by-step explanation:
put 4 instead of the h
50+4.20
50+80
130
HELP PLEASE the second one is a match question
Answer:
1)Coefficient
2)Dividend
3) Quotient
Step-by-step explanation:
A submarine dives below the surface, heading downward in nine moves. If each move downward was 180
feet where is the submarine after it is finished diving?
The submarine would be blank
feet below sea level, or blank
feet.
How do you do these two questions?
Answer:
(x − π)⁷ / 5040
(x − 1)³ / 16
Step-by-step explanation:
Taylor series expansion of a function is:
f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(x₀) / n! (x − x₀)ⁿ
where f⁽ⁿ⁾(x₀) is the nth derivative evaluated at x₀.
For the first problem, f(x) = sin x and x₀ = π. We want the seventh degree term, so n = 7.
The seventh degree term is therefore: f⁽⁷⁾(π) / 7! (x − π)⁷
Find the seventh derivative of sin x:
f(x) = sin x
f⁽¹⁾(x) = cos x
f⁽²⁾(x) = -sin x
f⁽³⁾(x) = -cos x
f⁽⁴⁾(x) = sin x
f⁽⁵⁾(x) = cos x
f⁽⁶⁾(x) = -sin x
f⁽⁷⁾(x) = -cos x
Evaluated at π, f⁽⁷⁾(x) = 1. So the seventh degree term is (x − π)⁷ / 5040.
For the second problem, f(x) = √x and x₀ = 1. We want the third degree term, so n = 3.
The third degree term is therefore: f⁽³⁾(1) / 3! (x − 1)³
Find the third derivative of √x:
f(x) = √x
f⁽¹⁾(x) = ½ x^-½
f⁽²⁾(x) = -¼ x^-³/₂
f⁽³⁾(x) = ⅜ x^-⁵/₂
Evaluated at 1, f⁽³⁾(x) = ⅜. So the third degree term is (x − 1)³ / 16.
sally has to pay 1/3 of her paycheck in tax. After paying tax, she spends 2/5 of the remainig money on rent. What fraction of her paycheck remains after she pays rent? Express your answer as a fraction in simplest form
9514 1404 393
Answer:
2/5
Step-by-step explanation:
After paying 1/3 in tax, 2/3 of Sally's paycheck remains.
After paying 2/5 of that, 3/5 of that 2/3 remains. The remaining fraction is ...
(3/5)(2/3) = 2/5
After the indicated payments, 2/5 of Sally's paycheck remains.
Answer:
2/5
Step-by-step explanation:
3/5 * 2/3 = 2/5
In addition to oxygen, several gases are in air. Carbon dioxide makes up 0.00039 of air. What is 0.00039 written as a percent?
Answer:
0.039%%%%%%%%%%%%%%
There are 25 pieces of fruit in a bowl and 4 of them are apples. What percentage of the
pieces of fruit in the bowl are apples?
Answer:
21%
Step-by-step explanation:
Each fruit is one percent so basically 25-4 which is 21 so 21%
QUICK HELP
What is the common ratio between successive terms in the sequence?
27, 9, 3, 1, 그 , ,
1
3
0
13
03
Answer:
the common ratio is
1/3
because
9*1/3=3
3*1/3=1
1*1/3=1/3
...
The common ratio is 1/3.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
The given sequence is
27, 9, 3, 1, 1/3, 1/9 and so on....
Since we know that
Common ratio (r) = Second term/First term
Therefore,
r = 9/27 = 3/9 ....
So, The answer will be 1/3.
Learn more about the ratio visit:
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# 5
Write an equation in slope-intercept
form to represent the line parallel to
9x + 3y = 8 passing through the point
(-1,-4).
y = -3x - 1
y = -3x - 7
y = 1/3x + 1/3
y = 1/3X -4
Answer:
y = -3x - 1
Step-by-step explanation:
it is the only line that passes through the point (-1, -4)
The product of two positive numbers is 48. the larger number is 13 more than the smaller. Find both numbers [Only an algebraic solution will be accepted.]
Answer:
Larger number:
16
Smaller number
3
Step-by-step explanation:
Larger number: 16
Smaller number: 3
Explanation:
Suppose the larger number is
a
and the smaller number is
b
.
You solve the following system of equations:
a⋅b=48
a−13=b
Since b is a −13, you can plug that into a⋅b=48, so...a⋅(a−13)=48
a 2−13a=48
a2−13a−48=0
Factor the polynomial:
(a−16)(a+3)=0
a=16 or a=−3a is positive so a=16.
We can now solve for b by plugging in a, so...16−13=b3=b We have a=16 and b=3, meaning that the larger number is 16 and the smaller number is 3.
-4x+6y=-7
-13x-2y=-4
Elimination or substitution
Answer:
substitution
Step-by-step explanation: