Meteorology: Normal Distribution The following problem is based on information from the National Oceanic and Atmospheric Administration (NOAA)

Environmental Data Service. Let x be a random variable that represents the average daily temperature

(in degrees Fahrenheit) in July in the town of Kit Carson, Colorado. The x distribution has a mean m of approximately 758F and standard deviation s of approximately 88F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table.

I II III IV Region under Normal Curve x°F Expected

% from Normal Curve Observed Number of Days in 20 Years m 2 3s # x , m 2 2s 51# x , 59 2.35% 16 m 2 2s # x , m 2s 59 # x , 67 13.5% 78 m 2s # x , m 67 # x , 75 34% 212 m # x , m 1s 75 # x , 83 34% 221 m 1s # x , m 1 2s 83 # x , 91 13.5% 81 m 1 2s # x , m 1 3s 91# x , 99 2.35% 12

(i) Remember that m 5 75 and s 5 8. 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 July temperature follows a normal distribution with m 5 75 and s 5 8 AppendixLO1