AnswersCA-Statistics and Probability BUsing the Central Limit TheoremQuestion 5
5
QuizMultiple Choice

Using the Central Limit Theorem

Question 5 • CA-Statistics and Probability B

The monthly cost for cell phones for plan Amazing has a mean of $39.17 with a standard deviation of $13.58, while the monthly cost for plan Best has a mean cost of $41.16 with a standard deviation of $7.18. A random sample of 37 phones is selected from plan Amazing, and a random sample of 40 phones is selected from plan Best. What is the probability that the mean cost for plan Amazing will be more than the mean cost for plan Best?

Answer
A
0.2134
B
0.7866
C
0.9741
D
0.9942

Explanation

The difference between the sample means (Amazing minus Best) has mean $39.17 − $41.16 = −$1.99. Its standard error is √(13.58²/37 + 7.18²/40) ≈ $2.50, so a difference of $0 corresponds to a z-score of (0 − (−1.99))/2.50 ≈ 0.79. The probability of a z-score greater than 0.79 is about 0.2134, so the answer is 0.2134.

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