Cloudiness in Breslau. In the paper “Cloudiness: Note on a Novel Case of Frequency” (Proceedings of the Royal Society of London, Vol. 62, pp. 287–290), K. Pearson examined data on daily degree of cloudiness, on a scale of 0 to 10, at Breslau (Wroclaw), Poland, during the decade 1876–1885. A frequency distribution of the data is presented in the following table. From the table, we find that the mean degree of cloudiness is 6.83 with a standard deviation of 4.28.

Degree Frequency Degree Frequency 0 751 6 21 1 179 7 71 2 107 8 194 3 69 9 117 4 46 10 2089 5 9

a. Consider simple random samples of 100 days during the decade in question. Approximately what percentage of such samples have a mean degree of cloudiness exceeding 7.5?

b. Would it be reasonable to use a normal distribution to obtain the percentage required in part

(a) for samples of size 5?

Explain your answer.

Extending the Concepts and Skills