Question

70 Homework:Section 8.1 Homework Save Score: 0.17 of 1 pt 10 of 13 (13 complete) HW Score: 51.44 % , 6.69 of 13 pts 8.1.27-T Question Help The acceptable level for insect fith in a certain food hem is 5 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food bem is obtained and results in a sample mean of x- 5.7 insect fragments per ten-gram portion. Complete parts (a) through (e) below (a) Why is the sampling distribution of x approximately normal? A The sampling distribution of x is approximately normal because the sample size is large enough The sampling distribution of x is assumed to be approximately normal CThe sampling dstribution of x is approximately normal because the population is normally distributed The sampling distribution of x is approximately normal because the population is normally distributed and the sample size is large enough. 0What is the mean and standard deviation of the sampling dstbution of x assuming 5 and n S (Round to three decimal places as needed) Enter your answer in the anewer bax and then click Check Answer parts remaining C Al MackookAir 7 Y G

Answer 1

Solution:

Given: Population mean =
u= 5

Population Standard Deviation =
0 = V5 = 2.236068

Sample size = n = 50
We have to find mean and standard deviation of sample distribution of sample mean $\bar{x}$ .

Since sample size n = 50 is large , we can use Central limit theorem which states that for large sample size n ,
sampling distribution of sample mean is approximately normal with mean of sample means:

Vi=

Me=5

and standard deviation of sample means is:

0i = n

oi= 2.236068 V50

0 = 2.236068 7.071068

0 = 0.316228

0= 0.316

( Round answer to specified number of decimal places)