7.43: Let denote the random variable for height and
for the sample mean. Then if
is the mean of
So the probability that the difference between the sample and population means does not exceed 0.5 inch is
per the empirical or 68/95/99.7 rule.
7.44: For a sample of size <em>n</em>, the sample standard deviation would be . We want to find <em>n</em> such that
Comparing to the equation from the previous part, this means we would need
so a sample of at least 157 men would be sufficient.