Familiarize yourself with Microsoft Excel’s statistical tools. Assuming that Z is the standard normal distribution:

(a) calculate Pr(1
Z
3) using the NORMSDIST function;

(b) calculate x such that Pr(Z
x) ¼ 0:95 using the NORMSINV function; (c)

calculate x such that Pr(Z  x) ¼ 0:15;

(d) generate 100 random numbers from the standard normal distribution using Tools/

Data Analysis/Random Number Generation. Calculate the sample mean and standard variance. How do they differ from the theoretical values of m ¼ 0 and s ¼ 1, respectively?

(e) Do the same for the standard uniform distribution as in (d).

(f ) Generate 100 normally distributed random numbers x using the function x ¼ NORMSINV(z) where z is taken from a sample of the standard uniform distribution. Explain why it is possible.
Calculate the sample mean and the standard deviation. How do they differ from the theoretical values of m and s, respectively?