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 between negative 0.99 and negative 0.32 and draw a sketch of the region.

Answer 1

Answer:  0.2134

Step-by-step explanation:

Given : Mean readings on thermometers =$\mu=0^{\circ}\ C$

Standard deviation = $\sigma=1.00^{\circ}\ C$

We assume that the readings on thermometers are normally distributed.

Let x be the random variable that represents the reading on a random thermometer.

To find z-score : $z=\dfrac{x-\mu}{\sigma}$

For x = -0.99

$z=\dfrac{-0.99-0}{1}=-0.99$

For x= -0.32

$z=\dfrac{-0.32-0}{1}=-0.32$

By using the standard normal distribution table , the probability that a randomly selected thermometer reads between -0.99 and -0.32 will be :-

$P(-0.99$