Question

Really cold cabin The dotplot shows the results of taking $300$SRSs of $10$temperature readings from a Normal population with $\mu =50$and $\sigma =3$and 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

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

Step-by-step solution

Given information

We have been given that

$$\begin{gathered} \mu =50 \\ \sigma =3 \end{gathered}$$

Temperature $=40°$F

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 $n$is$10$ 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 $3°F$.