Give your answer to the nearest gram

Question

A particular fruit's weights are normally distributed, with a mean of 567 grams and a standard deviation of 29 grams.

If you pick 8 fruits at random, then 17% of the time, their mean weight will be greater than how many grams?

Answer 1

Per the table, the z-score for probability 0.17 is z=

z=(x - mean)/D where D = stndDev/sqrt(N)

z*D + mean = x

D = 29/sqrt(8)

= 29*sqrt(8) / 8 <--- rationalizes the denomiantor

x = -0.95417 * 29*sqrt(8)/8 + 567

=