# MATHEMATICS

1. Given that Z is a standard normal random variable, compute the following probabilities.

a. P( 1.86 ≤ Z≤ 2.46)

b. P( Z > -1.45)

2. Given that Z is a standard normal random variable, find Z for each situation.

a. The area to the right of Z is 0.1736

b. The area between – Z and Z is 0.9678.

3. For borrowers with good credit scores, the mean debt for revolving and installment

accounts is $15,015 (BusinessWeek, March 20, 2006). Assume the standard deviation is

$3540 and that debt amounts are normally distributed.

a. What is the probability that the debt for a borrower with good credit is less than

$12,000?

b. What is the probability that the debt for a borrower with good credit is between $11,000

and $19,000?

4. In an article about the cost of health care, Money magazine reported that a visit to a hospi-

tal emergency room for something as simple as a sore throat has a mean cost of $328

(Money, January 2009). Assume that the cost for this type of hospital emergency room visit

is normally distributed with a standard deviation of $92. Answer the following questions

about the cost of a hospital emergency room visit for this medical service.

a. What is the probability that the cost will be more than $550?

b. What is the probability that the cost will be less than $275?

c. What is the probability that the cost will be between $300 and $450?

d. If the cost to a patient is in the lower 6% of charges for this medical service, what was

the cost of this patient’s emergency room visit?

5. Trading volume on the New York Stock Exchange is heaviest during the first half hour

(early morning) and last half hour (late afternoon) of the trading day. The early morning

trading volumes (millions of shares) for 13 days in January and February are shown here

(Barron’s, January 23, 2006; February 13, 2006; and February 27, 2006).

214 163 265 194 180

202 198 212 201

174 171 211 211

The probability distribution of trading volume is approximately normal.

a. Compute the mean and standard deviation to use as estimates of the population mean

and standard deviation.

b. What is the probability that, on a randomly selected day, the early morning trading

volume will be less than 180 million shares?