A paint company claims their paint will be completely dry within 45 minutes afte

Question

A paint company claims their paint will be completely dry within 45 minutes after application. Recently, customers have complained drying times are longer than the claimed 45 minutes. A consumer advocate group takes a random sample of 25 paint specimens and records their drying times. The average drying time x is 49. Consider dryng time, for all test specimens, to be normally distributed with ? = 9.

Suppose the claimed drying time is true, that is ? = 45 minutes, what is the probability of observing a sample mean of x = 49 or greater from a sample size of 25? (Round your answer to four decimal places.)

Explanation / Answer

First standardize the given mean value

formula of Standardize Z = (xbar - u) / (sd / sqrt(n))

Now Z score = (49 - 45) / (9 / sqrt(25))

= 4 / (9/5)

= 2.22

Now we need to find

p(xbar > 49) = p(Z > 2.22)

= 1 - p(Z < 2.22)

= 1 - 0.9868

= 0.0132

So Result is 0.0132

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