Review this example in which estimation is used. Then complete parts a through e below.

A company was considering producing a new snack chip. To see if there was enough interest, 1,000 randomly selected people tried the chips and were asked if they liked the chips or not, whether they would be likely to purchase them if they were available, and how often they would be likely to purchase them. Of the 1,000 people, 642 liked the chips, 271 stated they would purchase them once a month, and 137 stated they would purchase them once a week. The company inferred from these results that in a region with a population of 1,000,000 people, sales would be about 800,000 bags of chips per month.

a. What specifically was estimated?

A.

The number of people in the study that liked the chips

B.

The expected monthly sales of the chips in the region

C.

The expected monthly profit from selling the chips in the region

D.

The number of people in the study that would purchase the chips

b. What conclusion was reached using the estimation?

A.

271 people stated they would purchase the chips once a month

B.

Approximately 642 people liked the chips.

C.

Profits would be about $800,000 per month.

D.

Sales would be about 800,000 bags of chips per month.

c. Describe how the data were extracted and how they were used to produce the estimation.

A.

The data came from the number of bags people in the sample would buy and a proportion was used to produce the estimate.

B.

The data came from estimating the sales of the chips in a similar region and were used to produce the estimate.

C.

The data came from the number of people in the sample that would like the chips and a proportion was used to produce the estimate.

D.

The data came from sales records of similar chips in a similar region and were used to produce the estimate.

d. Keeping in mind the goal of the estimation, discuss whether you believe that the estimation was successful and why.

A.

The estimation was probably too low because people tend to enjoy snack foods.

B.

The estimation was probably successful because people tend to enjoy snack foods.

C.

The estimation was probably too high because people tend to lie about snack foods.

D.

The estimation was probably successful because it was based on market research.

e. Describe what inferences were drawn as a result of the estimation.

A.

The 1,000 people would purchase about 800 bags of chips per month, so 1,000,000 people would purchase about 800,000 bags.

B.

The 1,000 people would purchase about 300 bags of chips per month, so 1,000,000 people would purchase about 300,000 bags.

C.

Since monthly sales would be about 800,000 bags, producing the chips would be profitable.

D.

Since monthly sales would be about 800,000 bags, producing the chips would not be profitable.

2.

Suppose a random variable, x, has a uniform distribution with

a=1

and

b=9.

a. Calculate

P(1.5x7).

b. Determine

P(x<5).

c. Compute the mean,

,

and the standard deviation,

,

of this random variable.

d. Determine the probability that x is in the interval

(3).

a.

P(1.5x7)=enter your response here

(Simplify your answer.)

b.

P(x<5)=enter your response here

(Simplify your answer.)

c.

=enter your response here

(Simplify your answer.)

=enter your response here

(Round to three decimal places as needed.)

d.

P(3x+3)=enter your response here

(Round to three decimal places as needed.)