Question

A particular fruit's weights are normally distributed, with a mean of 428 grams and a standard deviation of 16 grams. If you pick 23 fruits at random, then 15% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

Answer 1

= 428

= 16

n = 23

SE = /

= 16/

= 3.3362

Mean weight greater than 15% corresponds to area = 0.5 - 0.15 = 0.35 from mid value to Z on LHS.

Table gives Z = - 1.04

So,

Z = - 1.04 = ( - 428)/3.3362

So,

= 428 - (1.04 X 3.3362)

= 428 - 3.4697

= 425

So,

Answer is:

425