Question

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Scores for a common standardized college aptitude test are normally distributed with a mean of 510 and a standard deviation of 110. 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 587.8. P(X> 587.8) = 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 8 of the men are randomly selected, find the probability that their mean score is at least 587.8. P(M> 587.8) = 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 8 men does result in a mean score of 587.8, 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 587.8. 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 587.8.

Answer 1

a) P(X > 587.8)

$\small = P(z > \frac{587.8-510}{110})$

= P(z > 0.70)

= 0.2397

b) P(M > 587.8)

$\small = P(z > \frac{587.8-510}{110/\sqrt{8}})$

= P(z > 2)

= 0.0227

c) Option B is correct.