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Hal and Jose are avid crossword puzzle solvers. Hal solves 48% of his crossword puzzles in under 30 minutes, while Jose solves 39% of his crossword puzzles in under 30 minutes. Suppose that Hal solves 22 crossword puzzles and Jose solves 26 crossword puzzles. Because [tex]np, n(1-P),[/tex] and [tex]n (1-P)[/tex] are all greater than 10, the Normal condition is met. Let [tex]H =[/tex] the proportion of Hal's crossword puzzles solved in under 30 minutes and [tex]J =[/tex] the proportion of Jose's crossword puzzles solved in under 30 minutes.

What is the probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's?

Find the z-table here.

A. 0.265
B. 0.449
C. 0.459
D. 0.735

Answer :

Final answer:

To find the probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's, we can use the normal distribution.

Explanation:

To find the probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's, we can use the normal distribution.

First, we calculate the mean and standard deviation for each proportion. For Hal, the mean is 0.48 and the standard deviation is √((0.48 × (1-0.48))/22). For Jose, the mean is 0.39 and the standard deviation is √((0.39 × (1-0.39))/26).

Once we have the mean and standard deviation for each proportion, we can standardize the proportions by subtracting the mean and dividing by the standard deviation. Then, we can use the standard normal distribution table to find the probability that Jose's standardized proportion is greater than Hal's standardized proportion.

The probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's is approximately 0.459.

Learn more about Probability here:

https://brainly.com/question/32117953

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