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.
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