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 limit as x approaches 2 of (3x+1)/(x^2-4) + (x-2)/(x^2-4)?

What is the range of the function f(x) = cos(2x) for x ∈ [-π/4, π]?

Math Question: What is the equation of a parabola with vertex at (3, 4) and axis of symmetry x = 3?

New questions in Mathematics

𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)

5(4x+3)=75

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?

The derivative of a power is obtained just by subtracting 1 from the power True or false

You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.

Find the derivatives for y=X+1/X-1

There are four times as many roses as tulips in Claire’s garden. Claire picked half of the number of roses and 140 roses were left in the garden. How many roses and tulips were in the Garden the first?