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)

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)

Question: What is the derivative of the function f(x) = ∫(5x^3, x^2) (3t^2 + 2t + 1) dt?

How many ways can we arrange the letters in the word "MATH" using all the letters?

What is the maximum value of the square root function y = √x in the domain [0, 100]?

New questions in Mathematics

𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)

a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour.

Revenue Maximization: A company sells products at a price of $50 per unit. The demand function is p = 100 - q, where p is the price and q is the quantity sold. How many units should they sell to maximize revenue?

Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)

3(4×-1)-2(×+3)=7(×-1)+2

A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had

The director of a company must transfer 6 people from the human resources department to the sales department, in order to sustain sales during the month of December. What is the probability that he will transfer only 2 of them?