Question

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. Assume 2.727% of the thermometers are rejected because they have readings that are too high and another 2.727% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

Answer 1

The Solution:

The question assumed that the readings on the thermometer are normally distributed with mean 0 degrees and standard deviation 1.00 degrees.

$2.727\text{ \%=0.02727}$

So, from the z-table, we have that

$\begin{gathered} P(Z<0.02727)=-1.923 \\ P(Z>0.02727)=1.923 \end{gathered}$

So, for readings that too low, we have

$\begin{gathered} P(ZFor readings that too high, we have[tex]\begin{gathered} P(Z<1.923)\Rightarrow Z=\frac{x-\mu}{\sigma} \\ \\ 1.923=\frac{x-0}{1} \\ \\ 1.923=x \end{gathered}$

To draw a sketch that shows the two readings that are cutoff values of the rejected thermometer, we have