The number of cookies in a shipment of bags are normally distributed, with a mean of 26 and a standard deviation of 4. What percent of bags of cookies will contain between 18 and 22 cookies?

Answer 1

To find the percentage of bags containing between 18 and 22 cookies, we need to first convert these values to z-scores using the formula:

z = (X - μ) / σ

Where:
X = value we are trying to convert
μ = mean of the distribution
σ = standard deviation of the distribution

For X = 18:
z = (18 - 26) / 4 = -2

For X = 22:
z = (22 - 26) / 4 = -1

Next, we will use a z-table or calculator to find the probabilities associated with these z-scores.

For z = -2, the z-table gives us a probability of approximately 0.0228.
For z = -1, the z-table gives us a probability of approximately 0.1587.

To find the probability of bags containing between 18 and 22 cookies, we subtract the probability of z = -2 from the probability of z = -1:

0.1587 - 0.0228 = 0.1359

Therefore, approximately 13.59% of bags of cookies will contain between 18 and 22 cookies.