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A small business ships specialty homemade candies to anywhere in the world. Past records indicate that...

A small business ships specialty homemade candies to anywhere in the world. Past records indicate that the weight of orders is normally distributed and the population standard deviation is 12 grams. Suppose a random sample of 16 orders is selected and each is weighed. The sample mean was found to be 110 grams with a standard deviation of 12.9 grams. Which of the following statements is​ true?

A The sampling distribution for the sample mean follows the ​t-distribution with 16 degrees of freedom.

B The sampling distribution for the sample mean is Normal with a mean of 110 grams and standard deviation of 3 grams.

C The sampling distribution for the sample mean is Normal with a mean of 110 grams and standard deviation of 12.9 grams.

D The sampling distribution for the sample mean follows the ​t-distribution with 15 degrees of freedom.

math   Statistics-And-Probability   
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Answer #1

Answer:

B The sampling distribution for the sample mean is Normal with a mean of 110 grams and standard deviation of 3 grams.

Explanation:

Mean for sampling distribution for the sample mean = Xbar = 110

df = 16

n = 17

Standard deviation for sampling distribution for the sample mean = σ/sqrt(n) = 12/sqrt(17) = 2.910428

Standard deviation for sampling distribution for the sample mean ≈ 3

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