# Random statistics problem – you plan to conduct a marketing

7.15 Given a normal distribution with and

if you select a sample of what is the probability m=100 Q = 10 n = 25

that is x is

**a. **less than 95?

**b. **between 95 and 97.5?

7.27 You plan to conduct a marketing experiment in which

students are to taste one of two different brands of soft

drink. Their task is to correctly identify the brand tasted.

You select a random sample of 200 students and assume that

the students have no ability to distinguish between the two

brands. (Hint: If an individual has no ability to distinguish

between the two soft drinks, then the two brands are equally

likely to be selected.)

**a. **What is the probability that the sample will have between

50% and 60% of the identifications correct?

b.The probability is 90% that the sample percentage is contained

within what symmetrical limits of the population

percentage?

**c. **What is the probability that the sample percentage of correct

identifications is greater than 65%?

**d. **Which is more likely to occur—more than 60% correct

identifications in the sample of 200 or more than 55%

correct identifications in a sample of 1,000? Explain.

8.1 If x = 85, o = 8and n = 64 construct a 95% confidence

interval estimate for the population mean, m

8.13 Assuming that the population is normally distributed,

construct a 95% confidence interval estimate for the population

mean for each of the following samples:

*Sample A:1o, 1o, 1o, 1o, 8o ,8o, 8o, 8o*

*Sample B:1,2,3,4,5,6,7,8*

Explain why these two samples produce different confidence

intervals even though they have the same mean and range.

8.17 The U.S. Department of Transportation requires tire

manufacturers to provide tire performance information on

the sidewall of a tire to better inform prospective customers

as they make purchasing decisions. One very important

measure of tire performance is the tread wear index, which

indicates the tire’s resistance to tread wear compared with a

tire graded with a base of 100. A tire with a grade of 200

should last twice as long, on average, as a tire graded with a

base of 100. A consumer organization wants to estimate the

actual tread wear index of a brand name of tires that claims

“graded 200” on the sidewall of the tire. A random sample of

N = 18 indicates a sample mean tread wear index of 195.3

and a sample standard deviation of 21.4.

**a. **Assuming that the population of tread wear indexes is

normally distributed, construct a 95% confidence interval

estimate for the population mean tread wear index

for tires produced by this manufacturer under this

brand name.

**b. **Do you think that the consumer organization should accuse

the manufacturer of producing tires that do not meet

the performance information provided on the sidewall of

the tire? Explain.

8.29 In a survey of 1,200 social media users, 76% said it is

okay to friend co-workers, but 56% said it is not okay to

friend your boss. (Data extracted from “Facebook Etiquette

at Work,” *USA Today*, March 24, 2010, p. 1B.)

**a. **Construct a 95% confidence interval estimate for the

population proportion of social media users who would

say it is okay to friend co-workers.

**b. **Construct a 95% confidence interval estimate for the

population proportion of social media users who would

say it is not okay to friend their boss.

8.35 If you want to be 99% confident of estimating the

population mean to within a sampling error of = or – 20and the

standard deviation is assumed to be 100, what sample size

is required?

8.39 If the manager of a paint supply store wants to estimate,

with 95% confidence, the mean amount of paint in a

1-gallon can to within = or – .004 gallon and also assumes that

the standard deviation is 0.02 gallon, what sample size is

needed?