# static

## static

﻿Tugas Kelompok ke-2
(Minggu 5 / Sesi 6)

CONTINUOUS PROBABILITY DISTRIBUTIONS

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

2. According to the Sleep Foundation, the average night’s sleep is 6,8 hours (Fortune, March 20, 2006). Assume the standard deviation is 0,6 hours and that the probability distribution is normal.
a. What is the probability that a randomly selected person sleeps more than 8 hours?
b. What is the probability that a randomly sleected person sleeps 6 hours or less?
c. Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep?

3. 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).

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?

c. What is the probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares?
d. How many shares would have to be traded for the early morning trading volume on a particular day to be among the busiest 5% of days?

4. For borrowers with good credit scores, the mean debt for revolving and installment accounts is \$15.015 (Business Week, March 20, 2006). Assume the standard deviation is \$3.540 and that debt amounts are normally distributed.
a. What is the probability that the debt for a randomly sleeced borrower with good credit is more than \$18.000?
b. What is the probability that the debt for a...