Scores for a common standardized college aptitude test are normally distributed with a mean of 483
and a standard deviation of
95
. Randomly-selected women are given a Preparation Course before taking this test.

a) If one of the women is randomly selected, find the probability that her score is at least 536.1 Enter your answer as a number accurate to 4 decimal places.

b) If twenty of the women are randomly selected, find the probability that their mean score is at least 536.1

c) I initially assumed that the Preparation Course had no effect on people's test scores. A random sample of twenty women does result in a mean score of more than 536.1. Is there strong evidence to support a claim that I was wrong -- and the Preparation Course is actually effective?

Yes. The probability indicates that -- if the Preparation Course has no effect -- it is highly unlikely that a randomly selected group of women would get a mean higher than 536.1 by chance.
No. The probability indicates that -- even if the Preparation Course has no effect -- it isn't unlikely to randomly select a group of women with a mean higher than 536.1 by chance.