Question

Assume the reading on thermometer are normally distributed with a mean of 0 degrees and a standard deviation of 100 degrees. Find the probability that a randomly selected thermometer reads between -2.28 and -1.69 and draw a sketch of the region

Answer 1

Let X =reading on thermometer.

Therefore, X follows normal distribution with mean = = 0 degrees and standard deviation = = 1.00 degrees

Here we want to find P(-2.28 < X < -1.69 ) = P( X < -1.69) - P(X < -2.28) ......( 1 )

By using Z table, we have :

P( X < -1.69) = 0.0455

P( X < -2.28 ) = 0.0113

Plug these values in equation ( 1 ), we get.

P(-2.28 < X < -1.69 ) = 0.0455 - 0.0113 = 0.0342 ( This is the final answer).