Scores for a common standardized college aptitude test are normally distributed with a mean of 510 and a standard deviation of 98. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.
If 1 of the men is randomly selected, find the probability that
his score is at least 588.4.
P(X > 588.4) =
If 9 of the men are randomly selected, find the probability that
their mean score is at least 588.4.
P(M > 588.4) =
Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help men do better. If the random sample of 9 men does result in a mean score of 588.4, is there strong evidence to support the claim that the course is actually effective?
P(X > 588.4)
= P((X - )/
> (588.4
-
)/
)
= P(Z > (588.4 - 510)/98)
= P(Z > 0.8)
= 1 - P(Z < 0.8)
= 1 - 0.7881
= 0.2119
P(M > 588.4)
= P((M - )/(
)
> (588.4 -
)/(
))
= P(Z > (588.4 - 510)/(98/))
= P(Z > 2.4)
= 1 - P(Z < 2.4)
= 1 - 0.9918
= 0.0082
Yes, The probability indicates that is unlikely that by chance, a randomly selected group of students would get a mean as high as 588.4
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