Answer:
1. It is not appropriate to use the normal curve, since np = 7.4 < 10.
2. The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.
Step-by-step explanation:
Binomial approximation to the normal:
The binomial approximation to the normal can be used if:
np >= 10 and n(1-p) >= 10
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The proportion of U.S. adults with high blood pressure is 0.2. A sample of 37 U.S. adults is chosen.
This means, respectively, that [tex]p = 0.2, n = 37[/tex]
Is it appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure?
np = 37*0.2 = 7.4 < 10
So not appropriate.
It is not appropriate to use the normal curve, since np = 7.4 < 10.
Part 2:
Now n = 82, 82*0.2 = 16.4 > 10, so ok
Mean and standard deviation:
By the Central Limit Theorem,
Mean [tex]\mu = p = 0.2[/tex]
Standard deviation [tex]s = \sqrt{\frac{0.2*0.8}{82}} = 0.0442[/tex]
Find the probability that more than 32% of the people in this sample have high blood pressure.
This probability is 1 subtracted by the pvalue of Z when X = 0.32. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.32 - 0.2}{0.0442][/tex]
[tex]Z = 2.72[/tex]
[tex]Z = 2.72[/tex] has a pvalue of 0.9967.
1 - 0.9967 = 0.0033
The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.
what is the horizontal cross section of the figure shown helpppp ill give brainliest answer
Answer:
Square
Step-by-step explanation:
Probably square
You look up at a 62 m tall building and find that the angle of elevation from the ground to the top of the building is 51 degrees. How far away from the building's base are you?
Answer:
Step-by-step explanation:
horizontal distance = 62/tan(51°) ≅ 50.2 m
The distance between the building base to a standing point is 50.20 m if the angle of elevation from the ground to the top of the building is 51 degrees.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.
It is given that:
You look up at a 62 m tall building and find that the angle of elevation from the ground to the top of the building is 51 degrees.
The angle = 51 degrees.
The height of the building = 62 m
Applying the tan ratio
tan51 = height of the building/distance between the building base to a standing point
tan51 = 62/x
x = 50.20 m
Thus, the distance between the building base to a standing point is 50.20 m if the angle of elevation from the ground to the top of the building is 51 degrees.
Learn more about trigonometry here:
brainly.com/question/26719838
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a woman spent 3/5 of her weekly salary on rent and 25% of her weekly salary on food. Her food cost $2500. How much did she spend on rent
Answer:
$6,000
Step-by-step explanation:
If her food costed $2500 and was 25%, then she had $10,000 to begin with. 3/5 of $10,000 is $6,000, so her rent costs $6,000.
Answer:
$6,000 on rent
Step-by-step explanation:
Find her weekly salary by dividing 2500 by 0.25
2500/0.25
= 10,000
Now, find how much she spent on rent by multiplying 10,000 by 3/5
10,000(3/5)
= 6,000
So, she spent $6,000 on rent
Find the perimeter. Simplify your answer.
3t+6
10t+7
6t-2
10t+4
Step-by-step explanation:
Perimeter is the sum of every side
6t-2 + 3t+6 + 10t+7 + 10t+4
= 6t + 3t + 10t + 10t -2 +6 +7 +4
= 29t + 15
A water-walking ball has a volume of approximately 904.32 cubic feet. What is the radius of the ball? (V = 4/3(pi)r^3)
Make sure you do put the unit with this answer rounded to the tenth if necessary.
Answer:
The radius of the ball is of 6 feet.
Step-by-step explanation:
The radius of the ball in spheric format is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In which r is the radius.
A water-walking ball has a volume of approximately 904.32 cubic feet. What is the radius of the ball?
Volume in cubic feet, so the radius will be in feet. We have to find r for which [tex]V = 904.32[/tex]. So
[tex]V = \frac{4\pi r^3}{3}[/tex]
[tex]904.32 = \frac{4\pi r^3}{3}[/tex]
[tex]r^3 = \frac{904.32*3}{4\pi}[/tex]
[tex]r = \sqrt[3]{\frac{904.32*3}{4\pi}}[/tex]
[tex]r = 6[/tex]
The radius of the ball is of 6 feet.
Assume that the probability of error-free transmission of a message over a communication channel is p. If a message is not transmitted correctly, a retransmission is initiated. This procedure is repeated until a correct transmission occurs. Such a channel is often called a feedback channel. Assuming that successive transmissions are independent, what is the probability that: a) No retransmission is required. b) Exactly two retransmissions are required
This question is incomplete, the complete question is;
Assume that the probability of error-free transmission of a message over a communication channel is p=0.9. If a message is not transmitted correctly, a retransmission is initiated. This procedure is repeated until a correct transmission occurs. Such a channel is often called a feedback channel. Assuming that successive transmissions are independent, what is the probability that:
a) No retransmission is required.
b) Exactly two retransmissions are required
Answer:
a) probability that No retransmission is required is 0.90
b) the probability that exactly two retransmissions are required is 0.009
Step-by-step explanation:
Given the data in the question;
the probability of error-free transmission of a message over a communication channel is p = 0.9
a) probability that No retransmission is required will be;
Let x represent the error-free transmission of a message
Now, the P( error-free_transmission_of_a_message) = 0.90
so;
P( X=0 ) = 0.90( 1 - 0.90 )⁰
P( X=0 ) = 0.90( 0.1 )⁰
P( X=0 ) = 0.90( 1 )
P( X=0 ) = 0.90
Therefore, probability that No retransmission is required is 0.90
b) Probability that exactly two retransmissions are required will be;
P( X=2 ) = 0.90( 1 - 0.90 )²
P( X=2 ) = 0.90( 0.1 )²
P( X=2 ) = 0.90( 0.01)
P( X=2 ) = 0.009
Therefore, the probability that exactly two retransmissions are required is 0.009
Mr. Williams is making wooden toy trucks for a craft show. He has 85 pieces of wood for the trucks
Each truck requires 6 pieces of wood.
Part A
How many toy trucks can Mr. Williams make? Enter your answer in the box.
00:00
Part B
How many pieces of wood will he have left? Enter your answer in the box.
Part A: He could make 14 toy trucks.
Divide 85 by 6.
85/6
14
(don't take any notice to the decimals)
Part B: He would have 1 piece of wood leftover.
6x14=84
Since Mr. Williams has 85 pieces of wood,
he would have 1 leftover.
Hope this helped!
pleaseeeee help ill give brainliest answerrrrr
Answer:
A= 360
Step-by-step explanation:
360
A train journey is approximately 150 miles.
How many centimetres will it be on a map with a scale of 30 miles = 1 cm?
==========================================================
Explanation:
The jump from 30 miles to 150 miles is "times 5", meaning 30*5 = 150.
So we need to multiply both sides of the equation
30 miles = 1 cm
by 5 and we get
5*(30 miles) = 5*(1 cm)
150 miles = 5 cm
--------------------
Another way to solve:
This involves proportions
Let x be the distance on the paper map that corresponds to 150 miles
(150 miles)/(x cm) = (30 miles)/(1 cm)
150/x = 30/1
150*1 = x*30 .... cross multiply
150 = 30x
30x = 150
30x/30 = 150/30 ... divide both sides by 30
x = 5 cm is the distance on the paper map
A boat travels 154 miles in 5 hours (with a constant speed). Approximately how much time will it take to travel 455 miles?
Answer:
14.77 hours.
Step-by-step explanation:
154÷5= 30.8
455÷30.8=14.76
A group of friends wants to go to the amusement park. They have $363 to spend on parking and admission. Parking is $5.50, and tickets cost $35.75 per person, including tax. How many people can go to the amusement park?
WILL GIVE BRAINEST!!! PLEASE HELP
Answer:
1.) The point (24,30) would not be on the line
2.) The point (12,13) would not be on the line either
4.) The slope is a fraction of 2/1
Bonus: y = (2/1)x - 2
Step-by-step explanation:
For question three, I looked at the (6,10) point on the graph and compared it with the (a,8) point. That showed me that the y coordinate always moves by 2. Then I looked at the (6,10) coordinate and the (a,8) coordinate and the (4,b) coordinate and saw that there was one x coordinate between 6 and 4 so it must be five. That means the x coordinate moves by 1.
Let me know if you need more help!
:)
An examination class of 55% of pupil scored 70% , if 54% scored above 70%. how many scored above 70%.
Answer:
54
Step-by-step explanation:
Let us assume the examination class is of 100 students
Now 55% scored 70% so 55% of 100 is 55
And, the 54% scored above 70% so 54% of 100 is 54
Therefore there are 54 who scored above 70%
Hence, the same would be considered and relevant too
plz help 52 points
For a scientific experiment, a physicist must make sure that the temperature of a metal does not get colder than −108°C or the metal will not be usable. The physicist changes the metal's temperature at a steady rate of −4°C per hour.
-3t < -78
÷-3 ÷-3
_________
t > 26
78÷26=3
Answer:
If the current temperature is 0 degrees C then:
27 hours
Step-by-step explanation:
108 divided by 4=27 hours.
Without writing the equation x^2 + y^2 + 24x – 26y+ 277 = 0 in the standard form, state whether the graph of this equation is a
parabola, circle, ellipse, or hyperbola.
a. parabola
c. hyperbola
b. ellipse
d. circle
Answer:
circle
Step-by-step explanation:
You can see there is a x^2 and y^2 and 24 x and 26 y meaning if you do complete the square you can write it as a circle in standard form
7. The prime factorization of which number is 2^5 x 5?
A) 50
B) 125
C) 160
D) 500
What is the value of the Expression
H-20 when h=60?
A:30
B:40
C:80
D:120
Answer:
BBBBBBBB
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Subtract 60-20 you'll get the answer
I will give you a brainliest if you answer this question 16
Answer:
0.75, 0.5, 0.25, 0.05
Hope it helps!!!
B.)0.75, 0.5,0.25,0.05
0.25
0.52
0.75 greatest
0.05 Least
Suppose that the length of research papers is uniformly distributed from 12 to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers.
A.) Give the distribution of X. (round your standard deviation to two decimal places. X
∼ N (18.5, _____)
B.) Give the distribution of SumX. Round your standard deviation to two decimal places. SumX
∼ (1017.5, _____).
C). Calculate the probability that the professor will need to read a total of more than 1080 pages. _____
Answer:
A.) X ~ N(18.5, 3.75)
B.) SumX ~ N(1017.5,27.8).
C.) 0.0122 = 1.22% probability that the professor will need to read a total of more than 1080 pages.
Step-by-step explanation:
Uniform distribution:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b.
The mean is given by:
[tex]M = \frac{a+b}{2}[/tex]
The standard deviation is given by:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The uniform distribution can be approximated to the normal, using its mean and its standard deviation.
Sum of n terms of a normally distributed variable:
The mean of the sum will be:
[tex]\mu_{s} = n\mu[/tex]
The standard deviation of the sum will be:
[tex]\sigma_{s} = \sqrt{n}\sigma[/tex]
Suppose that the length of research papers is uniformly distributed from 12 to 25 pages.
This means that [tex]a = 12, b = 25[/tex]
We survey a class in which 55 research papers were turned in to a professor.
This means that [tex]n = 55[/tex]
A.) Give the distribution of X.
The mean has already been given, and the standard deviation is:
[tex]S = \sqrt{\frac{(25-12)^2}{12}} = 3.75[/tex]
So
X ~ N(18.5, 3.75)
B.) Give the distribution of SumX.
Sum of 55 papers, the standard deviation will be of:
[tex]\sigma_{s} = \sqrt{55}*3.75 = 27.8[/tex]
So
SumX ~ N(1017.5,27.8).
C). Calculate the probability that the professor will need to read a total of more than 1080 pages
This is 1 subtracted by the pvalue of Z when X = 1080. So
[tex]Z = \frac{X - \mu_{s}}{\sigma_{s}}[/tex]
[tex]Z = \frac{1080 - 1017.5}{27.8}[/tex]
[tex]Z = 2.25[/tex]
[tex]Z = 2.25[/tex] has a pvalue of 0.9878
1 - 0.9878 = 0.0122
0.0122 = 1.22% probability that the professor will need to read a total of more than 1080 pages.
Determine whether m=27 is a solution to 20=m+3
Answer:
No.
Step-by-step explanation:
27+3=30, not 20.
Answer:
Nopeeee it is not
Step-by-step explanation:
20 = 27 + 3 ?
20 = 30 ?
Nope
m = 27 is not a solution
Please help. And show your work or your content answer will be removed and your points will be taken away from the one's you get from me.Thank you!
Answer:
“It’s not hard to steal points”.........................................so thx for points....................................bye
Step-by-step explanation:
Find the approximate circumference, in terms of π, of chicken pie that had a radius of 3.25 inches.
A) 3.25 πin.
B) 6.5 πin.
C) 20 πin.
D) 1.625 πin.
Answer:
B
Step-by-step explanation:
I Had this
Whats the square root of 128
Answer:
exact form: 8√2
decimal form: 11.3137
Answer:
i dont know
Step-by-step explanation:
Apply Theorem 22-B to solve for "b" State the proportion, and then the answer 27 12
Step-by-step explanation:
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zbajaibaaujabajaja
buwsusbvajz
two numbers have a sum of 527 and a difference of 195
Answer:
y+x = 527- 195
Step-by-step explanation:
correct me if im wrong pls anyone!
Simplify completely''''
Answer:
[tex]\displaystyle \frac{2x + 5}{x - 9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{2x^2 + 13x + 20}{x^2 - 5x - 36}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{(x + 4)(2x + 5)}{x^2 - 5x - 36}[/tex][Fraction] Factor denominator: [tex]\displaystyle \frac{(x + 4)(2x + 5)}{(x - 9)(x + 4)}[/tex][Fraction] Divide: [tex]\displaystyle \frac{2x + 5}{x - 9}[/tex](FILL IN THE BLANK)
Analyze the graph of the exponential decay function.
The initial value is _____
The base, or rate of change is _____
The domain is _____
can somebody help me please
Given parameters :
Camille is 7 years older than Donny Donny is 4 years younger than TommyTo find :
Total ages of the three peopleSolution with details :
Let us take the age of Donny as x years - i
According to the given question we have ,
Camille's age = x + 7 yearsTommy's age - 4 = Donny's age Tommy's age = Donny's age + 4Tommy's age = x + 4 ( from i )Total ages of three people = Sum of their ages
Camille's age + Donny's age + Tommy's age x + 7 + x + x + 4 3x + 11Maria found a circular rug for her floor. The rug has a circumference of 50.24 inches. Which formula should Maria use to help her find the diameter of the rug?
Answer:
She should use the formula [tex]C = \pi d[/tex] to find a diameter of 16 inches.
Step-by-step explanation:
The circunference of a circle is given by:
[tex]C = 2\pi r[/tex]
In which r is the radius, which is half the diameter. So, it can also be given by the following formula:
[tex]C = 2\pi \frac{d}{2} = \pi d[/tex]
In which d is the diameter.
Which formula should Maria use to help her find the diameter of the rug?
She should use this formula:
[tex]C = \pi d[/tex]
Since the circunference is 50.24 inches, the diameter will be of:
[tex]d = \frac{C}{\pi} = \frac{50.24}{\pi} = 16[/tex]
100) = +8 what is) when x = 102
Answer:
13
Step-by-step explanation:
10/2=5
5+8=13
