Question

A particular fruit's weights are normally distributed, with a mean of 656 grams and a standard deviation of 21 grams. If you pick 12 fruits at random, then 8% of the time, their mean weight will be greater than how many grams?

Answer 1

Solution,

Given that,

mean = = 656

standard deviation = = 21

n = 12

=   = 656

= / n = 21 / 12 = 6.062

Using standard normal table,

P(Z > z) = 8%

= 1 - P(Z < z) = 0.08

= P(Z < z ) = 1 - 0.08

= P(Z < z ) = 0.92

= P(Z < 1.41 ) = 0.92  

z = 1.41

Using z-score formula  

= z * +   

= 1.41 * 6.062 + 656

= 664.55 grams