The numbers of cookies in a shipment of bags are normally distributed, with a mean of 64 and a standard deviation of 4. What percent of bags of cookies will contain between 60 and 68 cookies?

Answer 1

To find the percentage of bags containing between 60 and 68 cookies, we need to find the area under the normal curve between these two values.

First, we need to standardize the values using the z-score formula:
z = (X - mean) / standard deviation

For X = 60:
z = (60 - 64) / 4 = -1

For X = 68:
z = (68 - 64) / 4 = 1

Next, we look up the z-scores in a standard normal distribution table to find the respective areas under the curve:
For z = -1, the area is approximately 0.1587
For z = 1, the area is approximately 0.8413

To find the area between these two values, we subtract the smaller area from the larger area:
0.8413 - 0.1587 = 0.6826

Therefore, approximately 68.26% of bags of cookies will contain between 60 and 68 cookies.