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

Step-by-step 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 :_

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

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

The required region is attached below .