Question

The number of chocolate chips in a an 18-ounce bag of Chips Ahoy! Chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cades of the US Air Force Academy.

1. What proportion of 18 ounce bags has more than 1000 chips?

Answer 1

Solution:

Given:The number of Chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips.

We have to find the proportion of 18 ounce bags has more than 1000 chips.

That is find:

P( X > 1000 ) = ...............?

Find z score for x = 1000

Thus we get:

P( X > 1000 ) = P( Z> -2.22 )

P( X > 1000 ) = 1 - P( Z <  -2.22 )

Look in z table for z = -2.2  and 0.02 and find corresponding area.

P( Z< -2.22 ) = 0.0132

Thus

P( X > 1000 ) = 1 - P( Z <  -2.22 )

P( X > 1000 ) = 1 - 0.0132

P( X > 1000 ) = 0.9868

Thus the proportion of 18 ounce bags has more than 1000 chips is 0.9868 or 98.68%.