Question

A statistician buys a pack of 10 new golf balls,
drops each golf ball from a height of one meter,
and measures the height in centimeters it returns
on the first bounce.

The ten values are:
79.9 80.0 78.9 78.5 75.6 80.5 82.5 80.1 81.6 76.7

Assume that y, the height (in cm) a golf ball bounces
when dropped from a one-meter height, is normal N(mu; sigma^2),
where the standard deviation sigma = 2.
(1) Assume a normal N(75, 1) prior for mu:
a. Find the posterior distribution of mu.
b. What is the Bayes estimate of mu?
c. Based on the posterior distribution, find P(mu >= 80)
d. Based on the posterior distribution, find a value c1
such that P(mu <= c1) = 0.025
e. Based on the posterior distribution, find a value c2
such that P(mu > c2) = 0.025

Answer 1