Question

The acceptable level for insect filth in a certain food item is 2 insect fragments​ (larvae, eggs, body​ parts, and so​ on) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of 2.3 insect fragments per​ ten-gram portion. Complete parts​ (a) through​ (c) below.

(b) What is the mean and standard deviation of the sampling distribution of x bar if mean is 2 and standard deviation is square root of 2

Answer 1

Solution :

Given that ,

mean = = 2

standard deviation = = 2

n = 50

The shape of the sampling distribution is approximately normal,

=   = 2

= / n = 2 / 50 = 0.28