Question

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 60 ​ten-gram portions of the food item is obtained and results in a sample mean of x overbarequals4.7 insect fragments per​ ten-gram portion. Complete parts ​(a) through ​(c) below. ​(a) Why is the sampling distribution of x overbar approximately​ normal? A. The sampling distribution of x overbar is approximately normal because the population is normally distributed. B. The sampling distribution of x overbar is approximately normal because the sample size is large enough. C. The sampling distribution of x overbar is assumed to be approximately normal. D. The sampling distribution of x overbar 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 of x overbar assuming mu equals 4 and sigmaequalsStartRoot 4 EndRoot​? mu Subscript x overbarequals nothing ​(Round to three decimal places as​ needed.) sigma Subscript x overbarequals nothing ​(Round to three decimal places as​ needed.) ​(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 4.7 insect​ fragments? ​P(x overbargreater than or equals4.7​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

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Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(2.71, TRUE)" to find the probability.