AnswersCA-Statistics and Probability BUsing the Central Limit TheoremQuestion 4
4
QuizMultiple Choice

Using the Central Limit Theorem

Question 4 • CA-Statistics and Probability B

The time needed for passengers to board the Twisting Thunder roller coaster is skewed right with a mean of 49 seconds and a standard deviation of 7.1 seconds. The time to board the Spiral Wonder roller coaster is skewed left with a mean of 44.8 seconds and a standard deviation of 3.7 seconds. What is the probability in a random sample of 32 times loading Twisting Thunder and 36 times loading Spiral Wonder that the mean time for Twisting Thunder is less than that of Spiral Wonder?

Answer
A
0.0042
B
0.0013
C
0.8584
D
0.9189

Explanation

Consider the difference between the sample means, Twisting Thunder minus Spiral Wonder. Its mean is 49 − 44.8 = 4.2 seconds, and its standard error is √(7.1²/32 + 3.7²/36) ≈ 1.40 seconds. The probability that this difference is less than 0 corresponds to z = (0 − 4.2)/1.40 ≈ −3.00, which has probability about 0.0013. Thus, the probability is 0.0013, choice B.

AI-written and checked against the verified answer.

Previous
Next

More from this Course

Quiz
10 verified answers

Using the Central Limit Theorem

Quiz
10 verified answers

Using the Central Limit Theorem

Quiz
10 verified answers

Estimating a Population Proportion