Question

A particular fruit's weights are normally distributed, with a mean of 718 grams and a standard deviation of 27 grams.

If you pick 12 fruits at random, then 16% 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 = = 718

standard deviation = = 27

n = 12

= 718

= / n = 27 / 12=7.79

Using standard normal table,

P(Z > z) =16 %

= 1 - P(Z < z) = 0.16  

= P(Z < z ) = 1 - 0.16

= P(Z < z ) = 0.84

z = 0.99

Using z-score formula  

= z * +

= 0.99 *7.79+718

= 726