1. The fuelconsumption, in miles pergallon, of all cars of a particular model has a mean of 30 and a standard deviation of 4 The population distribution can be assumed to be normal. A random sample of these cars is taken. Complete parts a and b below.

a. Find the probability that the sample mean fuel consumption will be fewer than 29

miles per gallon if samples of 1 ,4, and 9 are taken.

The probability for a sample of 1 observation is ?.

(Round to four decimal places asneeded.)

The probability for a sample of 4 observations is ?

(Round to four decimal places asneeded.)

The probability for a sample of 9 observations is ?

(Round to four decimal places asneeded.)

b. Explain why the three answers in part(a) differ in the way they do. Draw a graph to illustrate your reasoning.

As the sample sizeincreases, the mean of the sampling distribution of Upper X overbar (choose increases, stays the same , decreases) and the standard deviation (choose get closer to, get farther from)Therefore, the sample means tend to (choose increases, stays the same , decreases)get closer to get farther from the population mean. Since 29 is less than the populationmean, the portion of the sampling distribution of Upper X overbar that represents sample means fewer than 29 (choose remains about the same, gets larger, gets smaller )as the sample size increases.

2.A random sample of size 150 taken from a population yields a proportion equal to 0.33 Complete parts a through d below.

a. Determine if the sample size is large enough so that the sampling distribution can be approximated by a normal distribution.

Since np overbar=? nand n(1p overbar) =?, the sample size (is,is not,large enough.)

(Round to the nearest whole number asneeded.)

b. Construct a 99% confidence interval for the population proportion.

?-----?

(Round to three decimal places as needed. Use ascendingorder.)

c. Interpret the confidence interval calculated in part b.

Which statement below correctly interprets the confidenceinterval?

A.There is a 0.99 probability that the sample proportion is in the interval.

B.Of all the possible populationproportions, 99% are in the interval.

C.There is a 0.99 probability that the population proportion is in the interval.

D.There is 99% confidence that the population proportion is in the interval.

d. Produce the margin of error associated with this confidence interval.

e=?

(Round to three decimal places asneeded.)