MathMaster logo

MathMaster

  1. Home
  2. general
  3. scores for a common standardized college aptitude test are normally distributed with a mean of 499 and a standard deviatio
Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 499 and a standard deviation of 97. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 563.7. P(X > 563.7) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. If 9 of the men are randomly selected, find the probability that their mean score is at least 563.7. P(M > 563.7) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 9 men does result in a mean score of 563.7, is there strong evidence to support the claim that the course is actually effective? No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 563.7. Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 563.7.

211

likes
1057 views

Answer to a math question Scores for a common standardized college aptitude test are normally distributed with a mean of 499 and a standard deviation of 97. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 563.7. P(X > 563.7) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. If 9 of the men are randomly selected, find the probability that their mean score is at least 563.7. P(M > 563.7) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 9 men does result in a mean score of 563.7, is there strong evidence to support the claim that the course is actually effective? No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 563.7. Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 563.7.

Expert avatar
Maude
4.7
107 Answers
Given: X \sim N(499, 97^2)
We need to find:
1. P(X > 563.7)
2. P(M > 563.7) , where M is the mean of a sample of size n = 9

Step 1: Calculate the z-score:
z = \frac{563.7 - 499}{97} = \frac{64.7}{97} \approx 0.6680

1. P(X > 563.7) = P\left(Z > \frac{563.7 - 499}{97}\right) = P(Z > 0.6680) \approx 0.2525

Step 2: For the sample mean with n = 9 :
\sigma_M = \frac{97}{\sqrt{9}} = \frac{97}{3}
z_M = \frac{563.7 - 499}{\frac{97}{3}} = \frac{64.7}{\frac{97}{3}} \approx 2

2. P(M > 563.7) = P\left(Z > \frac{563.7 - 499}{97/3}\right) = P\left(Z > 2\right) \approx 0.0228

Therefore,
1. P(X > 563.7) \approx \boxed{0.2525}
2. P(M > 563.7) \approx \boxed{0.0228}

Since the probability of obtaining a sample mean of 563.7 or higher by chance alone is 0.0228, it is unlikely by chance alone, supporting the claim that the course is effective.

Hence, the answer is:
Yes. The probability indicates that it is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 563.7.

Frequently asked questions (FAQs)
What is the formula for calculating the z-score in statistics?
+
What is the value of sinh(2) - cosh(3) + tanh(1)?
+
What is the result of (3^2) * (3^4) + (3^3) ÷ (3^2)?
+
New questions in Mathematics
A pump with average discharge of 30L/second irrigate 100m wide and 100m length field area crop for 12 hours. What is an average depth of irrigation in mm unIt?
Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:
7273736363-8
2x-4y=-6; -4y+4y=-8
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6, what would be the standard deviation of that data set?
The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below. 23.0 21.2 23.5 23.6 20.1 24.3 25.2 26.9 24.6 22.6 26.1 23.1 25.8 24.6 24.3 24.1 24.8 22.1 22.8 24.5 (a) Find the z-scores for the largest measurement. (Round your answers to two decimal places.) z =
The equation of the circle that passes through (5,3) and is tangent to the abscissa axis at x=2 is a.(x-2)^2 (y 3)^2 = 9 b.(x-2)^2 (y-3)^2 = 9 c.(x-2)^2 (y-3)^2 = 4 d.(x-2)^2 (y 1)^2 = 4 e.(x-2)^2 (y-1)^2 = 4
Mrs. Emily saved RM10000 in a bank. At the end of the eighth year, the amount of money accumulated amounted to RM19992.71. If the bank pays an annual interest of x% for a year compounded every 6 months. Calculate the value of x.
prove that if n odd integer then n^2+5 is even
v Is the following statement a biconditional? If Shannon is watching a Tigers game, then it is on television.
Suppose you have a sample of 100 values from a population with mean mu = 500 and standard deviation sigma = 80. Given that P(z < −1.25) = 0.10565 and P(z < 1.25) = 0.89435, the probability that the sample mean is in the interval (490, 510) is: A)78.87% B)89.44% C)10.57% D)68.27%
How to factorise 5y^2 -7y -52
Find the area of a triangle ABC when m<C = 14 degrees, a = 5.7 miles, and b = 9.3 miles.
00 piece jigsaw puzzle. the completed puzzle is 10x10. each piech connects to at least 2 other pieces. i plan to assemble by taking pieces out of box one by one. if i've already taken out 2 pieces that dont directly connect, what is the minimum number of additional pieces that i need to draw to in order to guarentee that the original 2 pieces connect?
The blood types of individuals in society are as follows: A: 30%, B: 25%, AB: 20%, 0: 25%. It is known that the rates of contracting a certain disease according to blood groups are as follows: A: 7%, B: 6%, AB: 7%, 0: 4%. Accordingly, if a person selected by chance is known to have this disease, what is the probability of having blood group O?
Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?
calculate the product of 4 and 1/8
f(x)= 9-x^2 find (f(x+h)-f(x) )/h
An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?

You might be interested in