The manager of the claims department of a medical scheme can motivate to employ additional staff if she can show that the average number of claims being received for processing per day is more than 180. To motivate her need for additional staff, the manager selected a random sample of 100 days over the past year and recorded the number of claims received on each of these days.

(a) Use the Histogram option in Data Analysis to check the assumption of normality. Does the data appear to be normally distributed? Comment.

(b) Does the claims manager have good statistical evidence to support her request for additional staff? Conduct a hypothesis test for a single mean at the 1% level of significance. Show the null and alternative hypothesis and make a recommendation to the claims manager.