Meteorology: Normal Distribution Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for the town of Hana, Maui. The x variable has a mean m of approximately 688F and standard deviation s of approximately 48F (see reference in Problem 13). A 20-year study (620 January days)

gave the entries in the rightmost column of the following table.

I II III IV Region under Normal Curve x8F Expected

% from Normal Curve Observed Number of Days in 20 Years m 2 3s # x , m 2 2s 56 # x , 60 2.35% 14 m 2 2s # x , m 2s 60 # x , 64 13.5% 86 m 2s # x , m 64 # x , 68 34% 207 m # x , m 1s 68 # x , 76 34% 215 m 1s # x , m 1 2s 72 # x , 76 13.5% 83 m 1 2s # x , m 1 3s 76 # x , 80 2.35% 15

(i) Remember that m 5 68 and s 5 4. Examine Figure 6-5 in Chapter 6. Write a brief explanation for Columns I, II, and III in the context of this problem.

(ii) Use a 1% level of significance to test the claim that the average daily January temperature follows a normal distribution with m 5 68 and s 5 4.

AppendixLO1