# Given that Z is a standard normal random variable - 74276

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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?

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