AnswersCA-Statistics and Probability BUsing the Central Limit TheoremQuestion 7
7
QuizMultiple Choice

Using the Central Limit Theorem

Question 7 • CA-Statistics and Probability B

The number of pieces of cat food in a one-cup scoop is approximately Normally distributed with a mean of 344 pieces and a standard deviation of 16 pieces. If a random sample of 28 scoops of cat food is selected, what is the probability that the mean number of pieces will be more than 350 pieces?

Answer
A
0.0236
B
0.3538
C
0.6462
D
0.9764

Explanation

For the sample mean, the standard error is 16/√28 ≈ 3.02 pieces. The z-score for 350 pieces is (350 − 344)/3.02 ≈ 1.98. The probability of a z-score greater than 1.98 is about 0.0236, so the probability is 0.0236, choice A.

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