Math Question #5

Question

A particular fruit's weights are normally distributed, with a mean of 511 grams and a standard deviation of 29 grams.

If you pick 25 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

Find z for 90th percentile (1.28)

xbar = mean weight we want to find

z = (xbar - mu)/(s/sqrt(n)) = (xbar - 511)/(29/sqrt(25))

1.28 = (xbar - 511)/(29/sqrt(25))

1.28 = (xbar - 511)/5,8

xbar = 1.28 * 5.8 + 511 = 518.424 ~ 518 g