Question

A particular fruit's weights are normally distributed, with a mean of 678 grams and a standard deviation of 20 grams. If you pick 14 fruits at random, then 2% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

Answer 1

= 678

= 20

n = 14

SE = /

= 20/

= 5.3452

2% of the time, their mean weight will be greater than how many grams corresponds to area = 0.50 - 0.02 = 0.48 from mid value to Z on RHS.

Table of Area Under Standard Normal Curve gives Z = 2.055

So, we get:
Z = 2.055 = ( - 678)/5.3452

So,

= 678 + (2.055 X 5.3452)

= 678 + 10.9844

= 688.9844

= 689 (Round to the nearest gram)

So,

Answer is:

689