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Chapter 7: Q. 18 (page 456)

Really cold cabin The dotplot shows the results of taking 300SRSs of 10temperature readings from a Normal population with 渭=50and 蟽=3and recording the sample minimum each time. Suppose that the minimum of an actual sample is 40掳F. What would you conclude about the thermostat manufacturer鈥檚 claim? Explain your reasoning.

Short Answer

Expert verified

The cabin of the Starneses can stay considerably below freezing (32掳For 0掳C) for weeks at a time. The thermostat allows for temperature variance in the residence that follows a Normal distribution with an SRS of n=10readings over the course of a 24-hour period.

Step by step solution

01

Given information

We have been given that

渭=50蟽=3

Temperature =40掳F

02

Explanation

The Starneses' Colorado cabin can remain well below freezing (32掳F or 0掳C) for weeks at a time during the winter months. To keep the pipes from freezing, Mrs. Starnes sets the thermostat to 50掳F. The thermostat provides for temperature variance in the home that follows a Normal distribution with a value of 3掳F, according to the manufacturer. Mrs. Starnes tests this statement by taking an SRS of nis10 readings over the course of a 24-hour period with her digital thermometer. Assume that the thermostat is in functioning order and that the actual cabin temperatures follow a Normal distribution with a mean of 50掳F and a standard deviation of 3掳F.

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