The acceptable level for insect filth in a certain food item is 33 insect fragments​ (larvae, eggs, body​ parts, and so​ on) per 10 grams. A simple random sample of 5050 ​ten-gram portions of the food item is obtained and results in a sample mean of x overbarxequals=3.73.7 insect fragments per​ ten-gram portion. Complete parts ​(a) through ​(c) below. Question content area bottom Part 1 ​(a) Why is the sampling distribution of x overbarx approximately​ normal? A. The sampling distribution of x overbarx is approximately normal because the population is normally distributed. B. The sampling distribution of x overbarx is approximately normal because the population is normally distributed and the sample size is large enough. C. The sampling distribution of x overbarx is assumed to be approximately normal. D. The sampling distribution of x overbarx is approximately normal because the sample size is large enough. Your answer is correct. Part 2 ​(b) What is the mean and standard deviation of the sampling distribution of x overbarx assuming mu equals 3μ=3 and sigmaσequals=StartRoot 3 EndRoot3​? mu Subscript x overbarμxequals=33 ​(Round to three decimal places as​ needed.) Part 3 sigma Subscript x overbarσxequals=0.2450.245 ​(Round to three decimal places as​ needed.) Part 4 ​(c) What is the probability a simple random sample of 5050 ​ten-gram portions of the food item results in a mean of at least 3.73.7 insect​ fragments? ​P(x overbarxgreater than or equals≥3.73.7​)equals=0.00210.0021 ​(Round to four decimal places as​ needed.) Part 5 Is this result​ unusual? A. This result is notis not unusual because its probability is smallsmall. B. This result is notis not unusual because its probability is largelarge. C. This result isis unusual because its probability is largelarge. D. This result isis unusual because its probability is smallsmall.