Use the following information to answer the questions which follow. Draw and shade diagrams to help you find an answer.

Suppose residual heat is the difference between actual building temperature and thermostat setting (measured in degrees Fahrenheit). A negative residual heat, means the building temperature is below the setting--cooler than desired. As residual heat decreases (including becoming more negative). the building is becoming cooler. As residual heat increases (including becoming less negative), the building is warming up. Residual heat in a large department store building is a normal random variable with mean 1.2 degrees and standard deviation 0.8 degrees.
 

1.    What percent of the time is residual heat between -0.81 and 2.39 degrees?

2.    What percent of the time is residual heat less than -1.63 degrees?

3.    If most people feel comfortable, browse longer, and buy more when the
       temperature varies less than 1.5 degrees from the ideal (the thermostat setting),
       what percent of the time will customers feel uncomfortable?

4.    The middle 90% of residual heat values are between what two values? the middle
       95%? The middle 99%?

5.    The 90th percentile of residual heat readings is what value? (Note: the 90th
        percentile is the largest reading in the smallest 90% of the readings.
        Alternatively, it is the smallest value in the largest 10% of the readings).

6.    If the store wants the building temperature to be at least 72 degrees Fahrenheit
       97.5% of the time, determine the proper thermostat setting.

7.    Compare your diagrams and solutions with the problems in Worksheet 14. Which
       thermostat do you prefer, the one you just worked with or the one with residual
       heat that is standard normal?         Explain.
 
 

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