Question: A specific test is given to freshmen and sophomore classes at a certain college every year. It is know that the mean score for freshmen

A specific test is given to freshmen and sophomore classes at a certain college every year. It is know that the mean score for freshmen on the test is 58 with a standard deviation of 10 whereas the mean score for sophomore is 62 with a standard deviation of 15. A sample of 40 freshmen and 50 sophomore is 62 with a standard deviation of 15. A sample of 40 freshmen and 50 sophomore students are selected randomly.

a. What is the probability that sample mean of sophomore will exceed the sample mean of freshmen by less than 10?

b. What is the probability that sample mean of sophomore will exceed the sample mean of freshmen by more than 6?

c. What is the probability that two samples will differ in their mean scores by more than 2 points?

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