Problem #2 (20 points) - Two Short Probability Problems
a.) (12 points) A store opens for business at 9:00 AM and suppose that customers enter this
store according to a stationary Poisson process with a constant rate of 40 customers per
hour. Of these customers entering the school, 40% are female and 60% are males.
Compute the probability that the 5th male enters the store between 9:15 AM and 9:20 AM.
b.) (8 points) Suppose that a person invests in four stocks and that the return from each stock
are normal random variables with
$X_1 \sim N(20, 18)$, $X_2 \sim N(25, 10)$, $X_3 \sim N(15, 5)$ and $X_4 \sim N(8, 3)$
in units of hundreds of dollars. Compute the probability that the average return of all four
stocks
$X_{average} = \frac{X_1 + X_2 + X_3 + X_4}{4}$,
is between $15 hundred and $18 hundred.