1. Find
a. $P(Z < 1.5)$
b. $P(-1.05 < Z < 1.5)$
c. $P(Z > 1.5)$
2. Crookery Bank has analysed the monthly spending by its credit card customers and
found that it is normally distributed with a mean of $1000 and a standard deviation of
$150.
a. What is the probability that a customer will spend under $700?
b. What is the minimum amount spent by the top 10% of customers?
c. What is the maximum amount spent by the bottom 3.75% of customers?
3. Given $P(Z < -2.17) = 0.015$, use the rules of symmetry to find $P(-2.17 < Z < 2.17)$. (Just to be clear, you are to use the rules of symmetry in the slides and not the
Z tables to solve.)
4. Suppose that the waiting time for a license plate renewal at a local office of a state
motor vehicle department has been found to be normally distributed with a mean of
30 minutes and a standard deviation of 8 minutes.
i. What is the probability that a randomly selected individual will have a waiting
time of at least 10 minutes?
ii. What is the probability that a randomly selected individual will have a waiting
time between 15 and 45 minutes?
iii. Suppose that in an effort to provide better service to the public, the director of
the local office is permitted to provide discounts to those individuals whose
waiting time exceeds a predetermined time. The director decides that 15
percent of the customers should receive this discount. What number of
minutes do they need to wait to receive the discount?
5. Suppose that the distribution for a random variable X is normal with mean 15 and
standard deviation $\sigma$, and $P(X < 0) = 0.0773$. Rounded to two decimal places,
what is $\sigma$?
6. The monthly earnings of computer systems analysts are normally distributed with a
mean of $4,300. If the probability that a systems analyst earns a monthly income of
more than $6,140 is 0.015, what is the value of the standard deviation of the monthly
earnings of the computer systems analysts?
