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

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<a)=0.017`

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

Now,
`z=(a-\mu)/(\sigma)`

i.e.
`\pm2.12=(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.