1) The average male hippopotamus (Hippopotamus amphibius) weighs about 1500kg. Let's assume =1500 and =300kg.

a) Calculate Pr{Y>1676}

b) Now assume you have a sample of n=10 male hippos. Calculate Pr{>1676}.

c) Which probability is lower? Why?

2) Refer to problem 1. Now assume you take a sample of n=5 male hippos.

a) What is the probability of the sample average being within 150kg of the population mean (1500kg)?

In other words, you need to figure out Pr{ - 150 < < + 150}

b) What is the probability of the sample average being within 150kg of the population mean if the population mean is actually =1750 kg?

Are you surprised? Why or why not? You should make sure you understand what happened here.

c) Now assume a sample of n=14 male hippos and repeat (a).

What is the effect of sample size.?