Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 512 and a standard deviation of 111. 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 591.7.
P(X > 591.7) =

Enter your answer as a number accurate to 4 decimal places.

If 7 of the men are randomly selected, find the probability that their mean score is at least 591.7.
P(M > 591.7) =

Enter your answer as a number accurate to 4 decimal places.

If the random sample of 7 men does result in a mean score of 591.7, is there strong evidence to support the claim that the course is actually effective?

Yes. The probability indicates that is is unlikely that by chance, a randomly selected group of students would get a mean as high as 591.7.
No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 591.7.

Answer 1

This is a normal distribution question with

a)

P(x > 591.7)=?

The z-score at x = 591.7 is,

z = 0.718

This implies that

P(x > 591.7) = P(z > 0.718) = 1 - P(z < 0.718) = 1 - 0.7636213565920422

b)

Sample size (n) = 7

Since we know that

P(x > 591.7)=?

The z-score at x = 591.7 is,

z = 1.8997

This implies that

P(x > 591.7) = P(z > 1.8997) = 1 - P(z < 0.718) = 1 - 0.9712637498286429

c)

Yes. The probability indicates that is is unlikely that by chance, a randomly selected group of students would get a mean as high as 591.7.

PS: you have to refer z score table to find the final probabilities.

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