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

108 Answers

Given:

X \sim N(499, 97^2)

We need to find:
1.

P(X > 563.7)

P(M > 563.7)

, where

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

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

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}

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 chain rule for differentiating a composition of three functions?

What is the standard deviation of the following data set: 5, 10, 15, 20, 25?

Find the value of x when y = log2(x) intersects the x-axis on a graph.

New questions in Mathematics

A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?

How many percent is one second out a 24 hour?

How many kilometers does a person travel in 45 minutes if they move at a rate of 8.3 m/s?

A juice shop prepares assorted juices, for their juices they have 5 different types of fruit. How many types of assortments can be prepared in total, if it is considered an assortment to a juice made with two or more fruits?

The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?

Sean must chose a 6- digit PIN number for his online banking account.Each digit can be chosen from 0 to 9. How many different possible PIN numbers can sean chose.

The sum of two numbers is equal to 58 and the largest exceeds by at least 12. Find the two numbers