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 σ = 7.

Suppose the claimed drying time is true, that is μ = 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.)


You may need to use the z table to complete this problem.


Given the sample mean x = 49 was actually observed, is it reasonably that the average drying time is truly 45 minutes? Choose all that apply. (Select all that apply.)

No, it does not seem reasonable that the true average drying time is 45 minutes. It is unlikely to observe a sample mean this large or larger given the claim is true. It seems reasonable that the true drying time is 45 minutes. There is evidence the drying time is longer, on average. There is evidence the drying time is shorter, on average.

Answer 1

Given, n = 25, μ = 45 and σ = 7

We need to find P(x > 49)

P(Z>2.5) = 1 - P(Z<2.50)

From z distribution table, we can see that P(Z<2.50) = 0.9938 (See the screenshot below)

P(Z>2.5) = 1 - 0.9938

P(Z>2.5) = 0.0062

The probability of observing a sample mean of x = 49 or greater from a sample size of 25 is 0.0062

Since probability is less than 0.01 there is string evidence that drying time is greater than 45 minutes.

Correct options are:

No, it does not seem reasonable that the true average drying time is 45 minutes. It is unlikely to observe a sample mean this large or larger given the claim is true

There is evidence the drying time is longer, on average