Question

Assume the readings on thermometers are normally distributed with a mean of degrees and a standard deviation of 1.00degrees. Find the probability that a randomly selected thermometer reads greater than negative 0.69 and draw a sketch of the region.

Answer 1

Hence, the probability that randomly selected thermometer reads greater than negative 0.69 is 0.7549

Explanation:

Consider the provided information.

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

That means the value of σ = 1.

We need to find the probability that a randomly selected thermometer reads greater than negative 0.69

That means the value of mean is 0.

Normal distribution =
`z=(x-\mu)/(\sigma)`

Substitute the respective values as shown:

The probability should be greater that -0.6, Thus.

P(X>-0.6)=
`(-0.69-0)/(1)=-0.69`

Now use the standard normal table to find the value of P(Z>-0.69)

P(X>-0.6)=0.7549

Hence, the probability that randomly selected thermometer reads greater than negative 0.69 is 0.7549

The required region is shown in figure 1.