Probabilty and statistis

Question

Suppose that the weight of people in a specific town are normally distributed with the mean of 140 pounds and standard deviation of 20 pounds. Answer the following questions: 

1. Find the percentage of the people who weight less than 130 pounds.
2. Find the percentage of people who weight more than 160 pounds.

Answer 1

x = weight is N(140,20)

find P(x < 130)

z = (x - mean)/SD = (x - 140)/20

z is N(0,1)

transform inequality from N(140,20) to N(0,1):

P(x < 130) = P(z < (130-140)/20) = P(z < -0.5) = 0.3085 = 30.85%

find P(x > 160)

P(x > 160) = P(z > (160-140)/20) = P(z > 1) = P(z < -1) = 0.1587