The acceptable level for insect filth in a certain food item is 3 insect fragments(larvae, eggs, bodyparts, and soon) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of x=3.7 insect fragments perten-gram portion. Complete parts(a) through(c) below.

Click here to view the standard normal distribution table (page 1).LOADING...

Click here to view the standard normal distribution table (page 2).LOADING...

(a) Why is the sampling distribution of x approximatelynormal?

A.

The sampling distribution is assumed to be approximately normal.

B.

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

C.

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

D.

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

(b) What is the mean and standard deviation of the sampling distribution of x assuming =3 and =

3?

x=

nothing

(Round to three decimal places asneeded.)

x=

nothing

(Round to three decimal places asneeded.)

(c) What is the probability a simple random sample of 50 ten-gram portions of the food item results in a mean of at least 3.7 insectfragments?

P(x3.7)=

nothing

(Round to four decimal places asneeded.)

Is this resultunusual?

A.

This result is unusual because its probability is small.

B.

This result is unusual because its probability is large.

C.

This result isnot unusual because its probability is small.

D.

This result isnot unusual because its probability is large.

What might weconclude?

A.

Since this result isnot unusual, it isnot reasonable to conclude that the population mean is higher than 3.

B.

Since this result isnot unusual, it is reasonable to conclude that the population mean is higher than 3.

C.

Since this result is unusual, it isnot reasonable to conclude that the population mean is higher than 3.

D.

Since this result is unusual, it is reasonable to conclude that the population mean is higher than 3.

Click to select your answer(s).