Consider the undergraduate student population at Fordham. Suppose the true mean GPA in that population(mu)is 3.5, while the true standard deviation(sigma)is 0.15. In addition, the distribution of GPA is not normal (it is not symmetric and bounded between 0 and 4) in this population.

a.If you pick a random sample of40students, what is the probability to observea sample average below 3.5?

b.If you pick a random sample of40students, what is the probability to observea sample average between 3.5and 3.7?

c.If you pick a random sample of50students, what is the variance ofxbar(computed with 50 observations)?

d.If you pick a random sample of100students, what is the variance ofxbar(computed with100 observations)?

e.Which sample average is more informative, one computed with 50 or one computed with 100 observations? Explain.