Answers CA-Statistics and Probability B Using the Central Limit TheoremQuestion 5

5

QuizMultiple Choice

Using the Central Limit Theorem

Question 5 • CA-Statistics and Probability B

The distribution of the number of blocks a young child can stack before their tower falls is approximately Normally distributed with a mean of 12.7 blocks and a standard deviation of 1.4 blocks. If 6 of the child’s towers are randomly selected, what is the probability that the mean number of blocks is more than 11 blocks?

Answer

A

0.0015

B

0.1123

C

0.8877

D

0.9985

Explanation

For a sample of 6 towers, the standard deviation of the sample mean is 1.4/√6 ≈ 0.572 blocks. The z-score for 11 blocks is (11 − 12.7)/0.572 ≈ −2.97, so the probability that the mean is more than 11 is P(Z > −2.97) ≈ 0.9985. Thus, the correct choice is D, 0.9985.

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