Question

Potatoes: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.5 ounces and a standard deviation of 1.1 ounces. Round your answers to 4 decimal places.

(a) If one potato is randomly selected, find the probability that it weighs less than 7 ounces.


(b) If one potato is randomly selected, find the probability that it weighs more than 12 ounces.


(c) If one potato is randomly selected, find the probability that it weighs between 7 and 12 ounces.

Answer 1

Part a)

P ( X < 7 )
Standardizing the value

Z = ( 7 - 8.5 ) / 1.1
Z = -1.36

P ( X < 7 ) = P ( Z < -1.36 )
P ( X < 7 ) = 0.0869

Part b)

P ( X > 12 ) = 1 - P ( X < 12 )
Standardizing the value

Z = ( 12 - 8.5 ) / 1.1
Z = 3.18

P ( Z > 3.18 )
P ( X > 12 ) = 1 - P ( Z < 3.18 )
P ( X > 12 ) = 1 - 0.9993
P ( X > 12 ) = 0.0007

Part c)

P ( 7 < X < 12 )
Standardizing the value

Z = ( 7 - 8.5 ) / 1.1
Z = -1.36
Z = ( 12 - 8.5 ) / 1.1
Z = 3.18
P ( -1.36 < Z < 3.18 )
P ( 7 < X < 12 ) = P ( Z < 3.18 ) - P ( Z < -1.36 )
P ( 7 < X < 12 ) = 0.9993 - 0.0863
P ( 7 < X < 12 ) = 0.9129