Question

A particular fruit's weights are normally distributed, with a mean of 336 grams and a standard deviation of 11 grams.

If you pick 17 fruit at random, what is the probability that their mean weight will be between 331 grams and 345 grams? State your answer to four decimal places.

Answer 1

Solution:

Given: A particular fruit's weights are normally distributed, with a mean of 336 grams and a standard deviation of 11 grams.

That is:  

Sample Size= n= 17

We have to find: the probability that their mean weight will be between 331 grams and 345 grams

Find z scores:

and

Thus we get:

Look in z table for z = 3.3 and 0.07 as well as for z = -1.8 and 0.07 and find area.

P( Z< 3.37) = 0.9996

and

P( Z< -1.87) = 0.0307

Thus