Scores for a common standardized college aptitude test are normally distributed with a mean of 485 and a standard deviation of 101. 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 530.7. P(X > 530.7) = 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 11 of the men are randomly selected, find the probability that their mean score is at least 530.7. P(M > 530.7) = 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 the random sample of 11 men does result in a mean score of 530.7, is there strong evidence to support the claim that the course is actually effective? 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 530.7.No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 530.7.

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Asked Jan 27, 2020
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Scores for a common standardized college aptitude test are normally distributed with a mean of 485 and a standard deviation of 101. 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 530.7.
P(X > 530.7) =
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 11 of the men are randomly selected, find the probability that their mean score is at least 530.7.
P(M > 530.7) =
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 the random sample of 11 men does result in a mean score of 530.7, is there strong evidence to support the claim that the course is actually effective?
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 530.7.
No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 530.7.

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Expert Answer

Step 1

Given data

Mean (µ) = 485

Standard deviation (σ) = 101

If 1 of the men is randomly selected, probability that his score is at least 530.7  is given by

P(X ≥ 530.7)

Changing into standard normal variate

Statistics homework question answer, step 1, image 1
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Step 2

If 11 of the men are randomly selected, probability that their mean score is at least 530.7 is given by
P(M > 530.7)

Changing into standard normal variate

Statistics homework question answer, step 2, image 1
fullscreen
Step 3

Probability is greater than 0.05, so it indicates that is possible by chance alone to randomly select a group of students with a mean as high as 530.7.

So, correct option i...

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Hypothesis Testing

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