Question

Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.3 ounces.

Suppose Carl bags his potatoes in randomly selected groups of 6. What percentage of these bags should have a mean potato weight between 7.5 and 8.5 ounces? Enter your answer as a percentage rounded to one decimal place.
%

Answer 1

Solution :

Given that ,

mean =   = 8

standard deviation = = 1.3

n = 6

= 8

=  / n= 1.3 / 6=0.53

P(7.5<     < 8.5) = P[(7.5-8) /0.53 < ( - ) /   < (8.5-8) / 0.53)]

= P(-0.94 < Z <0.94 )

= P(Z <0.94 ) - P(Z < -0.94)

Using z table

=0.8264 - 0.1736

=0.6528

= 65.28%