A particular fruit's weights are normally distributed, with a mean of 747 grams and a standard deviation of 8 grams.

Question

If you pick 19 fruits at random, then 12% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

Answer 1

xbar = sample mean weight

747 = population mean weight

8 = population standard deviation

19 = sample size

z statistic for sample mean = (xbar - 747)/ (8/sqrt(19))

z-score corresponding to 12th percentile = -1.175

-1.175 = (xbar - 747)/(8/sqrt(19))

-1.175 = (xbar - 747)/1.835

-1.175*1.835 + 747 = xbar

xbar = 744 (nearest gram)