finding probability

Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 166.5-cm and a standard deviation of 2.2-cm.

Find the probability that the length of a randomly selected steel rod is between 159.9-cm and 170.9-cm.
P(159.9-cm < X < 170.9-cm) =


Enter your answer as a number accurate to 4 decimal places.

Answer 1

Prob( 159.9 < x < 170.9) =

 

Prob(  (159.9 - 166.5)/2.2 <   z <  (170-166.5)/2.2) =

 

Prob( -3 < z < 2.045) =

 

Prob(z < 2.045) - Prob ( z < -3) =

 

0.9741 - 0.0013 = 0.9728