Question

A particular fruit's weights are normally distributed, with a mean of 471 grams and a standard deviation of 31 grams.

If you pick 21 fruits at random, then 9% 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 = = 471

standard deviation = = 31

n = 21

= = 471

= / n = 31 / 21 = 6.76

Using standard normal table,

P(Z > z) = 9 %

= 1 - P(Z < z) = 0.09  

= P(Z < z ) = 1 - 0.09

= P(Z < z ) = 0.91

= P(Z < z ) = 0.91  

z = 1.341

Using z-score formula  

= z * +   

= 1.341 * 6.76 + 471

= 480.07

= 481