Question

A particular fruit's weights are normally distributed, with a mean of 258 grams and a standard deviation of 35 grams.

If you pick 16 fruits at random, then 10% 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 = = 258

standard deviation = = 35

n = 16

= 258

= / n = 35/ 16=8.75

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.9

z = 1.28 ( using z table)

Using z-score formula  

= z * +   

=1.28*8.75+258

= 269