Question

A particular fruit's weights are normally distributed, with a mean of 615 grams and a standard deviation of 36 grams. If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

Answer 1

= 615 g

= 36 g

n = 22

For sampling distribution of mean, = = 615 g

=

=

= 7.675

P( < A) = P(Z < (A - )/)

3% of the time, let the mean weight will be greater than W grams

P( > W) = 0.03

P(Z < W) = 1 - 0.03 = 0.97

P(Z < (W - 615)/7.675) = 0.97

Take value of Z corresponding to the probability of 0.9700 from standard normal distribution table.

(W - 615)/7.675 = 1.88

W = 629 g

3% of the time, their mean weight will be greater than 629 grams