Question

Assume that the readings on the thermometers are normally distributed with a mean of 0 C and a standard deviation of 1 C. A thermometer is randomly selected and tested. If 1.7% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.

Answer 1

Answer: -2.12°C

Step-by-step explanation:

Let x denotes the reading of the thermometers .

We assume that the readings on the thermometers are normally distributed.

Let a be the reading that separates the rejected thermometers from the others.

Given: Population mean : $\mu=0$

Standard deviation: $\sigma= 1$

Also, $P(x$

By using the z-table , the z-value corresponds to the p-value (one -tailed)0.017 is $\pm2.12$.

Now, $z=\dfrac{a-\mu}{\sigma}$

i.e. $\pm2.12=\dfrac{a-0}{1}$

i.e. $\pm2.12=a$

For left tailed , $a=-2.12$

It means the reading that separates the rejected thermometers from the others = -2.12°C.