Question

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between -2.05 and −1.18

Answer 1

SOLUTION:

From given data,

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between -2.05 and −1.18

Where,

Mean = = 0°C

Standard deviation = = 1.00°C

Z = (X-) / = (X-0) / 1

The probability that a randomly selected thermometer reads between -2.05 and −1.18

P(-2.05 < X < −1.18) = P((-2.05 -0) / 1 <(X-) / < (−1.18-0) / 1)

P(-2.05 < X < −1.18) = P(-2.05 < Z < -1.18 )

P(-2.05 < X < −1.18) = P(Z < -1.18 ) - P(Z < -2.05 )

P(-2.05 < X < −1.18) = 0.11900 - 0.02018 (From Standard Normal Distribution as shown below)

P(-2.05 < X < −1.18) = 0.09882

The probability that a randomly selected thermometer reads between -2.05 and −1.18 is 0.09882