Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight,X,of each item is recorded.Prior experience has shown that the weight has a probability distribution with μ = 180 grams and σ = 75 grams.Which of the following is true about the sampling distribution of the sample mean if a sample size of 15 is selected?
A) The shape of the sample distribution is approximately normal.
B) The standard deviation of the sampling distribution is 75 grams.
C) The mean of the sampling distribution is 180 grams.
D) All of the above are correct.

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample mean ($\bar{X}$) is equal to the population mean ($\mu$), which is given as 180 grams. The Central Limit Theorem suggests that the sampling distribution will approach a normal distribution as the sample size increases, but with a sample size of 15, it's not guaranteed to be approximately normal unless the population distribution is normal. The standard deviation of the sampling distribution (the standard error) is $\sigma / \sqrt{n}$, not 75 grams, making option B incorrect.

Suppose a Sample of N = 50 Items Is Drawn