Question: The score of all applicants taking an aptitude test required by law school have a normal distribution with mean 420 and standard deviation 100. A random sample of twenty-five scores is taken.

1. Find the probability that the sample mean score is bigger than 450.
2. Find the probability that the sample mean score is between 400 and 450.
3. Find the probability that the sample standard deviation is less than 67?
4. The probability is 0.10 that the sample mean score is bigger than what number?
5. The probability is 0.15 that the sample mean score is less than what number?
6. The probability is 0.05 that the sample standard deviation of the scores is bigger than what number?
7. The probability is 0.05 that the sample standard deviation of the scores is less than what number?

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