Mean weight!!!!!

Question

A particular fruit's weights are normally distributed, with a mean of 791 grams and a standard deviation of 8 grams.

If you pick 15 fruits at random, then 7% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

I did this, and received 791.265 as an answer. Why is this wrong?

Answer 1

7% of time greater than a certain value means 93% of the time less than a certain value, which is the 93rd percentile.

93rd percentile for z-stat = 1.47

mean = 791

SD = 8

sample size = 15

standard error (SE) = 8/sqrt(15) = 2.07

z-stat = (xbar - pop mean)/SE

1.47 = (xbar - 791)/2.07

xbar = 1.47*2.07 + 791 = 794.0429