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yoonie is a personnel manager in a large corporation. each month she must review 16 of the employees. the time that takes to do a review has a bell shaped distribution with a mean of four hours and a standard deviation of 1.2 hours. what is the probability that the average time of 16 reviews will take yoonie from 3.5 to 4.25 hours?

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varshamittal029

The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.

The random variable X is defined as the time it takes her to complete one review.

The random variable X follows a Normal distribution with parameters μ = 4 hours and σ = 1.2 hours.

A random sample of n = 16 reviews are selected as a set.

Compute the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours as follows:

P(3.5 < X < 4.25) = P(3.5-4/1.2√16 < x- μ /σ/√n < 4.25-4/1.2/√16)

=P(-1.67 < Z < 0.83)

= P(Z < 0.83) - (P(Z < -1.67)

= 0.7967 - 0.0475

= 0.7492

Thus, the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.

Learn more about Probability here:

brainly.com/question/25688842

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