Hello Tutor, I'm struggling with the concept of this topic. Could you please explain thoroughly how to solve the following?

1.) The average supermarket lemon weighs about 100 grams. Let's assume = 100 and = 15.

a) Calculate Pr{Y > 107}

b) Now assume you take a sample of n = 16 lemons. Calculate Pr{ > 107}.

c) Which probability is lower? Why?

-Now assume you have n=9 lemons

d.)What is the probability of the sample average being within 7 grams of the population mean (100 g)?

e.)What is the probability of the sample average being within 7 grams of the population mean if the population mean is actually = 90 g?

f.)Now assume a sample of n = 25 lemons and repeat (d). What is the effect of sample size?