The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.0 5.2 3.0 4.8 Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of the paint.

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

Step-by-step explanation:

First we have to find the sample mean and the sample standard deviation.

We have 15 measurements. Using a calculator, the mean is and the standard deviation is of .

Now, we have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.1448

The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 3.79 - 0.54 = 3.25 hours

The upper end of the interval is the sample mean added to M. So it is 3.79 + 0.54 = 4.33 hours

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

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