statistics homework

Question

The population of weights of a particular fruit is normally distributed, with a mean of 698 grams and a standard deviation of 25 grams. If 27 fruits are picked at random, then 14% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

Answer 1

use z transformation formula to solve problem

let xbar = mean weight; want to find xbar representing 14th percentile

z = (xbar - pop mean)/pop std dev/(sqrt(sample size) = (xbar - 698)/(25/sqrt(27)) = (xbar - 698)/4.81

from table you can find what z corresponds to the 14th percentile (probability of 0.14), which is -1.409

so

-1.409 = (xbar - 698)/4.81

-1.409 * 4.81 + 698 = xbar

691.22 = xbar

rounded to nearest gram, xbar = 691 g