Question

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.5 ounces and a standard deviation of 0.8 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 10 ounces.


(c) If one potato is randomly selected, find the probability that it weighs between 7 and 10 ounces.

Answer 1

Solution :

Given that ,

mean = = 8.5

standard deviation = =0.8

n = 1

= 8.5

=  / n = 0.8/ 1=0.8

(A)P( < 7) = P[( - ) / < (7 -8.5) /0.8 ]

= P(z < -1.875)

Using z table  

=0.0304

probability=0.0304

(B)

P( >10 ) = 1 - P( <10 )

= 1 - P[( - ) / < (10 -8.5) /0.8 ]

= 1 - P(z <1.875 )

Using z table

= 1 - 0.9696

= 0.0304

probability= 0.0304

(c)

P(7<    <10 ) = P[(7 -8.5) /0.8 < ( - ) / < (10 -8.5) /0.8 )]

= P(-1.875 < Z <1.875 )

= P(Z <1.875 ) - P(Z < -1.875)

Using z table

=0.9696 -0.0304

=0.9392

probability= 0.9392