Question

A particular fruit's weights are normally distributed, with a mean of 683 grams and a standard deviation of 36 grams.

If you pick 24 fruits at random, then 3% 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 = = 683

standard deviation = = 36

n = 24

= 683

= / n =36/ 24=7.3485

Using standard normal table,

P(Z > z) = 3%

= 1 - P(Z < z) = 0.03

= P(Z < z ) = 1 - 0.03

= P(Z < z ) = 0.97

= P(Z < 1.88 ) = 0.97

z = 1.88

Using z-score formula  

= z * +   

= 1.88 *7.3485+683

=696.81

=697