Question

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.

Find the probability of obtaining a reading between -2.75°C and 0°C. P ( − 2.75 < Z < 0 ) =

Answer 1

Given:

Mean = 0

Standard deviation = 1

To find P(-2.75 < Z < 0)

P(-2.75 < Z < 0) = P(Z <= 0) - P(Z <= -2.75)

We can find ot this probability using the Z table or technology.

Let's find out this probability using excel.

First of all, find out P(Z <= 0)

Use the following excel command.

=NORMSDIST(Z)

=NORMSDIST(0)

We will get, P(Z <= 0) = 0.5

NowLet's find out P(Z <= -2.75)

Use the following excel command.

=NORMSDIST(Z)

=NORMSDIST(-2.75)

We will get, P(Z <= -2.75) = 0.00298

P(-2.75 < Z < 0) = P(Z <= 0) - P(Z <= -2.75)

= 0.5 - 0.00298

P(-2.75 < Z < 0) = 0.49702