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

(a) Why is the sampling distribution ofapproximately normal?

A.

The sampling distribution is assumed to be approximately normal.

B.

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

C.

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

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 ofassumingand ?

mew=

sigma=

(c) What is the probability a simple random sample often-gram portions of the food item results in a mean of at leastinsect fragments?

P(x>4.6)

_______(Round to four decimal places as needed.)

Is this result unusual?

A.

This resultunusual because its probability is .

B.

This resultunusual because its probability is .

C.

This resultunusual because its probability is .

D.

This resultunusual because its probability is .

What might we conclude?

A.

Since this resultunusual, itreasonable to conclude that the population mean is higher than .

B.

Since this resultunusual, itreasonable to conclude that the population mean is higher than .

C.

Since this resultunusual, itreasonable to conclude that the population mean is higher than .

D.

Since this resultunusual, itreasonable to conclude that the population mean is higher than .