Question

A particular fruit's weights are normally distributed, with a mean of 520 grams and a standard deviation of 40 grams.

If you pick 27 fruits at random, then 11% of the time, their mean weight will be greater than how many grams?

Answer 1

Given that,

mean = = 520

standard deviation = = 40

n = 27

= 520

= / n = 40/ 27=7.6980

Using standard normal table,

P(Z > z) = 11%

= 1 - P(Z < z) = 0.11  

= P(Z < z ) = 1 - 0.11

= P(Z < z ) = 0.91

= P(Z < 1.34) = 0.91  

z = 1.34 using z table

Using z-score formula  

= z * +   

=1.34 *7.6980+520

= 530.3153