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 : [tex]\mu=0[/tex]
Standard deviation: [tex]\sigma= 1[/tex]
Also, [tex]P(x<a)=0.017[/tex]
By using the z-table , the z-value corresponds to the p-value (one -tailed)0.017 is [tex]\pm2.12[/tex].
Now, [tex]z=\dfrac{a-\mu}{\sigma}[/tex]
i.e. [tex]\pm2.12=\dfrac{a-0}{1}[/tex]
i.e. [tex]\pm2.12=a[/tex]
For left tailed , [tex]a=-2.12[/tex]
It means the reading that separates the rejected thermometers from the others = -2.12°C.
