The acceptable level for insect filth in a certain food item is 4 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 = 4.8 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 of x is assumed to be approximately normal. B. The sampling distribution of x is approximately normal because the population is normally distributed and the sample size is large enough. C. The sampling distribution of x is approximately normal because the population is normally distributed. D. The sampling distribution of x 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 μ=4 and σ = 4? μx = nothing (Round to three decimal places as needed.) σx = nothing (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 4.8 insect fragments? P( x ≥ 4.8) = nothing (Round to four decimal places as needed.)
The acceptable level for insect filth in a certain food item is
4 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
x
=
4.8 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 of
x is assumed to be approximately normal.
B.
The sampling distribution of
x is approximately normal because the population is
C.
The sampling distribution of
x is approximately normal because the population is normally distributed.
D.
The sampling distribution of
x 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
μ=4 and
σ
=
4?
μx
=
nothing
(Round to three decimal places as needed.)
σx
=
nothing
(Round to three decimal places as needed.)
(c) What is the
40 ten-gram portions of the food item results in a mean of at least
4.8 insect fragments?
P(
x
≥
4.8)
=
nothing
(Round to four decimal places as needed.)
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