Question

The acceptable level for insect filth in a certain food item is

55

insect fragments​ (larvae, eggs, body​ parts, and so​ on) per 10 grams. A simple random sample of

4040

​ten-gram portions of the food item is obtained and results in a sample mean of

x overbarxequals=5.55.5

insect fragments per​ ten-gram portion. Complete parts​ (a) through​ (c) below.Click here to view the standard normal distribution table (page 1).

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

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​(a) Why is the sampling distribution of

x overbarx

approximately​ normal?

A.

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

B.

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

Your answer is correct.

C.

The sampling distribution is assumed to be approximately normal.

D.

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

​(b) What is the mean and standard deviation of the sampling distribution of

x overbarx

assuming

mu equals 5μ=5

and

sigmaσequals=StartRoot 5 EndRoot5​?

mu Subscript x overbarμxequals=nothing

​(Round to three decimal places as​ needed.)

Answer 1

a. Here n=40>30, so as per central limit theorem distribution of sample mean is normal as n>30.

So correct answer here is

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

b. Now here and

So mean of sampling distribution of is and standard deviation is