Question

Assume the readings on thermometers are normally distributed with a mean of 0degreesc and a standard deviation of 1.00degreesc. find the probability that a randomly selected thermometer reads greater than 2.07 and draw a sketch of the region.

Answer 1

Let Z be the reading on thermometer. Z follows Standard Normal distribution with mean μ =0 and standard deviation σ=1

The probability that randomly selected thermometer reads greater than 2.07 is

P(z > 2.07) = 1 -P(z < 2.07)

Using z score table to find probability below z=2.07

P(Z < 2.07) = 0.9808

P(z > 2.07) = 1- 0.9808

P(z > 2.07) = 0.0192

The probability that a randomly selected thermometer reads greater than 2.07 is 0.0192