Next, you can use your *z*-table or the *p*–*z* converter to find the probability of obtaining a *z*-value this large or larger, assuming that we are sampling from a normal distribution with a mean of 500. This *p*-value corresponds to the probability of obtaining a sample mean of 530 or larger from a sample of 10 people randomly selected from a normally distributed population with a mean of 500.

What is the probability of a *z* score of .95 or more?

#### p = 0.050

*Incorrect!* We set the alpha level to .05. If our *p*-value is less than .05 we will reject the null hypothesis. The *p*-value corresponds to the area of the *z* distribution that is greater than our observed*z*-value. You can use the *p-z* converter to find this value.

#### p = 0.171

**Correct!** The probability of observing a *z*-score equal to .95 or greater is .171. If the null hypothesis is true such that the training program has no effect, the probability is .171 that the mean for a random sample of 10 graduates is 530 or greater.

#### p = 0.329

*Incorrect!* The probability of observing a *z*-score between zero and .95 is .329. We wish to know the probability of observing a *z*-score as large or larger than .95.

#### p = 0.342

*Incorrect!* The probability of observing a *z*-score .95 or farther from the mean is .342. This is a two-tailed probability. In our application we are interested only in the upper tail of the distribution.

#### p = 0.829

*Incorrect!* The probability of observing a *z*-score less than or equal to .95 is .829. We would like to know the probability of observing a *z*-score greater than or equal to .95.

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