# Interpret the key results for Tolerance Intervals (Normal Distribution)

Complete the following steps to interpret tolerance intervals.

## Step 1: Assess the normality of the data

Minitab provides tolerance intervals for the normal method and the nonparametric method. If you can safely assume that your data follow a normal distribution, then you can use the normal method tolerance interval. If you cannot safely assume that your data follow a normal distribution, then you must use the nonparametric method tolerance interval.

To determine whether you can assume that the data follow a normal distribution, compare the p-value from the normality test to the significance level (α). A significance level of 0.05 indicates a 5% risk of concluding that the data do not follow a normal distribution when the data do follow a normal distribution.

P-value ≤ α: The data do not follow a normal distribution (Reject H0)
If the p-value is less than or equal to the significance level, you can conclude that your data do not follow a normal distribution. In this case, you must use the nonparametric method tolerance interval.
P-value > α: You do not have enough evidence to conclude that the data do not follow a normal distribution (Fail to reject H0)
If the p-value is larger than the significance level, you do not have enough evidence to conclude that the data do not follow a normal distribution. In this case, you can use the normal method tolerance interval. Key Results: P-ValueIn these results, the p-value is 0.340, which is greater than the significance level of 0.05. Because you can assume that your data follow a normal distribution, you can use the normal method tolerance interval.

## Step 2: Examine the tolerance interval from the appropriate method

Minitab provides tolerance intervals for the normal method and the nonparametric method. You can create a two-sided tolerance interval, or a one-sided tolerance interval that provides an upper bound or a lower bound.
Two-sided
Use a two-sided interval to determine the interval that contains a certain percentage of the population measurements.
Upper bound
Use an upper bound to determine the interval that indicates that a certain percentage of population measurements will not be greater than an upper limit.
Lower bound
Use a lower bound to determine the interval that indicates that a certain percentage of population measurements will not be less than a lower limit.