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 6060 ​ten-gram portions of the food item is obtained and results in a sample mean of x overbarxequals=5.35.3 insect fragments per​ ten-gram portion. Complete parts ​(a) through ​(c) below.       Part 1 (a) Why is the sampling distribution of x̄ approximately​ normal? A. The sampling distribution of x̄ is approximately normal because the sample size is large enough. Part 2 (b) What is the mean and standard deviation of the sampling distribution of x̄ assuming μ = 5 and σ = √5? μₓ̄ =    5 (Round to three decimal places as​ needed.) Part 3 σₓ̄ =    0.645 (Round to three decimal places as​ needed.) Part 4 (c) What is the probability a simple random sample of 60 ​ten-gram portions of the food item results in a mean of at least 5.3 insect​ fragments? P(x̄ ≥ 5.3) =    (You need to calculate this probability)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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
6060
​ten-gram portions of the food item is obtained and results in a sample mean of
x overbarxequals=5.35.3
insect fragments per​ ten-gram portion. Complete parts ​(a) through ​(c) below.
 
 
 

Part 1 (a) Why is the sampling distribution of x̄ approximately​ normal?

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

Part 2 (b) What is the mean and standard deviation of the sampling distribution of x̄ assuming μ = 5 and σ = √5?

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

Part 3 σₓ̄ =    0.645 (Round to three decimal places as​ needed.)

Part 4 (c) What is the probability a simple random sample of 60 ​ten-gram portions of the food item results in a mean of at least 5.3 insect​ fragments?

P(x̄ ≥ 5.3) =    (You need to calculate this probability)

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