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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 μ=50and σ=3and recording the sample minimum each time. Suppose that the minimum of an actual sample is 40°F. What would you conclude about the thermostat manufacturer’s claim? Explain your reasoning.

Short Answer

Expert verified

The cabin of the Starneses can stay considerably below freezing (32°For 0°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

μ=50σ=3

Temperature =40°F

02

Explanation

The Starneses' Colorado cabin can remain well below freezing (32°F or 0°C) for weeks at a time during the winter months. To keep the pipes from freezing, Mrs. Starnes sets the thermostat to 50°F. The thermostat provides for temperature variance in the home that follows a Normal distribution with a value of 3°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°F and a standard deviation of 3°F.

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