Question

Suppose it is known that the weights of a certain group of individuals are approximately normally distributed with a mean of 140 pounds and a standard deviation of 25 pounds. What is the probability that a person picked at random from this group will weigh between 100 and 170 pounds?

Answer 1

Given = 140 , = 25

We convert this to standard normal as   

P(X < x) = P( Z < ( X - ) / )      

P ( 100 < X < 170 ) = P(X < 170) - P(X < 100)

= P ( Z < ( 170 - 140 ) / 25 ) - P ( Z < ( 100 - 140 ) / 25 )      

= P ( Z < 1.2) - P ( Z < -1.6 )       

= 0.8849 - 0.0548 (From Z table)

= 0.8301