Suppose the mean GPA of BYU-Idaho students is 3.7 and the standard deviation is

Question

Suppose the mean GPA of BYU-Idaho students is 3.7 and the standard deviation is 0.9. It is well known that this distribution is left-skewed. Use this information to answer questions 5 and 6. 5. If you take a random sample of 64 BYU-Idaho students, what is the mean and standard deviation of the distribution of sample means of these GPA scores? mean = 3.7 standard deviation = 0.9 mean = 0.463 standard deviation = 0.9 mean = 3.7 standard deviation = 0.113 mean = 0.463 standard deviation = 0.113 6. What is the probability that the mean GPA for 64 randomly selected BYU-Idaho students will be less than 3.5? Suppose the mean GPA of BYU-Idaho students is 3.7 and the standard deviation is 0.9. It is well known that this distribution is left-skewed. Use this information to answer questions 5 and 6.

Explanation / Answer

(5) mean=3.7 (stay the same)

standard deviation= s/vn =0.9/sqrt(64) = 0.1125

Answer: mean = 3.7 standard deviation = 0.113

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(6) P(xbar<3.5)

=P((xbar-mean)/(s/vn) < (3.5-3.7)/ 0.1125)

=(Z<-1.78)

=0.0375 (from standard normal table)

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