Question

A particular fruit's weights are normally distributed, with a mean of 446 grams and a standard deviation of 32 grams. If you pick 3 fruits at random, then 8% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

Answer 1

Given that,

mean = = 446

standard deviation = = 32

n = 3

= 446

= / n = 32/ 3=18.48

Using standard normal table,

P(Z > z) = 8%

= 1 - P(Z < z) = 0.08

= P(Z < z ) = 1 - 0.08

= P(Z < z ) = 0.92

= P(Z < z ) = 0.92

z = 1.41

Using z-score formula  

= z * +   

= 1.41 *18.48+446

=472