**(1)**The frequency distribution shows the results of 200 test scores. Are the test scores normally distributed? Use (alpha) α = 0.05 Complete parts (a) through (d).

**Class Boundaries, Frequency f.**

**49.5 – 58.5, 20.**

**58.5 – 67.5, 60.**

**67.5 – 76.5, 80.**

**76.5 – 85.5, 35.**

**85.5 – 94.5, 5.**

Using a chi-square goodness-of-fit test, you can decide, with some degree of certainty, whether a variable is normally distributed. In all chi-square tests for normality, the null and alternative hypotheses are as follows.

H0: The test scores have a normal distribution.

Ha: The test scores do not have a normal distribution.

**a.** Find the expected frequencies?.

**b.** Determine the critical value, χ20, and the rejection region?.

**c.** Calculate the test statistic.

**d. **Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim