**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) is less than 1.57?

b) is greater than 1.84?

c) is between 1.57 and 1.84?

d) is less than 1.57 or greater than 1.84?

**6.5**

Given a normal distribution with µ = 100 and σ = 10, what is the probability that:

a) Χ 75?

b) X 70?

c) X 80 or X 110?

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 coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as a normal random variables 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 $60.00

c) What proportion of the households spent between $40.00 and $50.00?

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 µ = 240 seconds and σ = 10 seconds.

a) What is the probability that a call lasted less than 180 seconds?

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 Caterpillar’s $20.5 billion to ExxonMobil’s $347.4 billion. The market capitalization values for the 30 companies that comprise the DJIA are stored in DowMarketCap.

Decide whether the market capitalization of companies in the DJIA appears to be approximately normally distributed by

a) Comparing data characteristics to theoretical properties.

b) Constructing a normal probability plot.

c) Constructing a histogram.