Question

Assume the readings on thermometers are normally distributed with a mean of 0 degrees C and a standard deviation of 1.00 degrees C. Find the probability that a randomly selected thermometer reads greater than 2.17 and draw a sketch of the region.

Answer 1

Answer: 0.0035

Explanation:

Given : The readings on thermometers are normally distributed with a mean of 0 degrees C and a standard deviation of 1.00 degrees C.

i.e.
`\mu=0` and
`\sigma= 1`

Let x denotes the readings on thermometers.

Then, the probability that a randomly selected thermometer reads greater than 2.17 will be :_

`P(X>2.7)=1-P(\xleq2.7)\\\\=1-P((x-\mu)/(\sigma)\leq(2.7-0)/(1))\\\\=1-P(z\leq2.7)\ \ [\because\ z=(x-\mu)/(\sigma)]\\\\=1-0.9965\ \ [\text{By z-table}]\ \\\\=0.0035`

Hence, the probability that a randomly selected thermometer reads greater than 2.17 = 0.0035

The required region is attached below .