Question

The number 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 64 and 68 cookies?

Answer 1

To solve this problem, we need to standardize the values using z-scores and then use a z-table to find the area under the normal curve between those z-scores.

First, we find the z-score for 64:

z = (64 - 64) / 4 = 0

Next, we find the z-score for 68:

z = (68 - 64) / 4 = 1

Now, we can use the z-table to find the area under the normal curve between these two z-scores. The area represents the percentage of bags of cookies that will contain between 64 and 68 cookies.

From the z-table, we find that the area between 0 and 1 is 0.3413. Multiply this by 100 to get the percentage:

0.3413 x 100 = 34.13%

Therefore, approximately 34.13% of bags of cookies will contain between 64 and 68 cookies.