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 2.72.7​% of the thermometers are rejected because they have readings that are too high and another 2.72.7​% 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 diagram is attached below.

Explanation:

A normal distribution mean 0 and standard deviation 1 is known as the standard normal distribution.

So, the readings on the thermometers (denoted by Z) follows N (0, 1).

It is provided that 2.7​% of the thermometers are rejected because they have readings that are too high and 2.7​% are rejected because they have readings that are too low.

This implies that:

`P(Z<-z)=0.027\ \text{and}\ P(Z>z)=0.027`

The value of z associated to both these probabilities are:

z = 1.93.

That is,

`P(Z<-1.93)=0.027\ \text{and}\ P(Z>1.93)=0.027`

*Use a z-table.

The diagram for the two readings that are cutoff values separating the rejected thermometers from the others is attached below.