4.The acceptable level for insect filth in a certain food item is 5 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40 ten-gram portions of the food item is obtained and results in a sample mean of x = 5.4 insect fragments per ten-gram portion. Complete parts (a) through (c) below.

(a)

Why is the sampling distribution of x approximately normal?

A.

The sampling distribution is approximately normal because the sample size is large enough.

B.The sampling distribution is approximately normal because the popluation is normally distributed.

C.The sampling distribution is assumed to be approximately normal.

D.

The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough.

(b) What is the mean and standard deviation of the sampling distribution of x assuming = 5 and = 5 ?

x =5(Round to three decimal places as needed.)

x =0.3535

(Round to three decimal places as needed.)

(c) What is the probability a simple random sample of 40 ten-gram portions of the food item results in a mean of at least 5.4 insect fragments?

P(x 5.4) =(Round to four decimal places as needed.)

Is this result unusual?

A.

This result is unusual because its probability is small.

B.This result is unusual because its probability is large.

C.This result is not unusual because its probability is large.

D.This result is not unusual because its probability is small.

What might we conclude?

A.

Since this result is unusual, it is reasonable to conclude that the population mean is higher than 5.

B.Since this result is not unusual, it is reasonable to conclude that the population mean is higher than 5.

C.

Since this result is not unusual, it is not reasonable to conclude that the population mean is higher than 5.

Since this result is unusual, it is not reasonable to conclude that the population mean is higher than 5.