6.1 Given a standardized normal distribution (with a mean
of 0 and a standard deviation of 1, as in Table E.2), what is the probability that
a. Z is less than 1.57?
b. Z is greater than 1.84?
c. Z is between 1.57 and 1.84?
d. Z is less than 1.57 or greater than 1.84?
6.5 Given a normal distribution m = 100 and s = 10
what is the probability that
a. X > 75?
b. X < 70?
c. X < 80 or X > 100?
d. Between what two X values (symmetrically distributed around the mean) are 80% of the values?
6.7 In a recent year, about two-thirds of U.S. households
purchased ground coffee. Consider the annual ground cof-
fee expenditures for households purchasing ground coffee,
assuming that these expenditures are approximately distrib-
uted as a normal random variable with a mean of $65.16 and
a standard deviation of $10.00.
a. Find the probability that a household spent less than $35.00. b. Find the probability that a household spent more than
c. What proportion of the households spent between $40.00
d. 99% of the households spent less than what amount?
6.11 A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Bricks and Clicks
Computer Corporation indicates that the length of these
calls is normally distributed, with m = 240 seconds and
s = 40 seconds.
a. What is the probability that a call lasted less than 180
b. What is the probability that a call lasted between 180 and 300 seconds?
c. What is the probability that a call lasted between 110 and 180 seconds?
d. 1% of all calls will last less than how many seconds?
6.19 Thirty companies comprise the DJIA. Just how big
are these companies? One common method for measuring
the size of a company is to use its market capitalization,
which is computed by multiplying the number of stock
shares by the price of a share of stock. On June 19, 2009, the market capitalization of these companies ranged from...
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