Question

The number of chocolate chips in a popular brand of cookie is normally distributed with a mean of 21 chocolate chips per cookie and a standard deviation of 1.3 chips. When the cookies come out of the oven, only the middle 90% in terms of the number of chocolate chips are acceptable (the rest are considered defective). What are the cutoff numbers for the number of chocolate chips in acceptable cookies? (Give your answers to three decimal places)

Answer 1

Middle 90% means 5% bottom and 5% top are excluded.

Given that

mean = 21

standard deviation (sd) = 1.3

Using percentile table, we will note down the z score corresponding to 5th percentile and 95th percentile

so, we get

z score for 5th percentile = -1.645

and z score for 95th percentile = 1.645

Lower cut off value =

and

upper cut off value =