Q. 18 Really cold cabin The dotplot sh... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 7: Q. 18 (page 456)

Really cold cabin The dotplot shows the results of taking $300$ SRSs of $10$ temperature readings from a Normal population with $渭 = 50$ and $蟽 = 3$ and 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 ( $32 掳 F$ or $0 掳 C$ ) for weeks at a time. The thermostat allows for temperature variance in the residence that follows a Normal distribution with an SRS of $n = 10$ readings over the course of a $24$ -hour period.

Step by step solution

Given information

We have been given that

$渭 = 50 蟽 = 3$

Temperature $= 40 掳$ F

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 $n$ 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 $50 掳 F$ and a standard deviation of $3 掳 F$ .