Refer to the Transactions of the ASME (June 2004) study on predicting daily natural gas consumption using temperature, Exercise 5.32. Recall that the researchers showed that the daily July temperature in Buenos Aires, Argentina, is normally distributed with and . Consider a random sample of n daily July temperatures from the population and let S² represent the sample variance.

Use Table 8 of Appendix B to estimate the following probabilities:

a. P(S² > 14.4) when n = 10
b. P(S² > 33.3) when n = 5
c. P(S² > 16.7) when n = 22

Data from exercise 5.32

The Transactions of the ASME (June 2004) presented a model for predicting daily natural gas consumption in urban areas. A key component of the model is the distribution of daily temperatures in the area. Based on daily July temperatures collected in Buenos Aires, Argentina, from 1944 to 2000, researchers demonstrated that the daily July temperature is normally distributed with μ = 11°C and σ = 3.1°C. Suppose you want to use temperature to predict natural gas consumption on a future July day in Buenos Aires.