the standard 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 60 and 68 cookies?

Answer 1

To solve this problem, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

Where:

x = the value we want to find the probability for (in this case, between 60 and 68)
μ = the mean of the distribution (64)
σ = the standard deviation of the distribution (4)

For the lower end (60 cookies):

z = (60 - 64) / 4 = -1

For the upper end (68 cookies):

z = (68 - 64) / 4 = 1

Now, we can use a z-table or calculator to find the probability of being between these two z-scores. Using a standard normal distribution table, we can find that the area between -1 and 1 is approximately 0.6827. This means that approximately 68.27% of bags of cookies will contain between 60 and 68 cookies.

Answer 2

are you sure thats correct

Answer 3

I apologize for my mistake. The correct approach to solving this problem is:

First, we can calculate the z-scores for the lower and upper limits of the desired range:

z1 = (60 - 64) / 4 = -1
z2 = (68 - 64) / 4 = 1

Next, we can look up the area under the standard normal distribution curve between these two z-scores using a z-table or calculator. The area between -1 and 1 is approximately 0.6827, as I previously stated.

Finally, we can multiply this area by 100% to obtain the percentage of bags of cookies that will contain between 60 and 68 cookies:

0.6827 x 100% = 68.27%

Therefore, approximately 68.27% of bags of cookies will contain between 60 and 68 cookies. I apologize for any confusion caused by my earlier message.

Answer 4

are you sure

Answer 5

Yes, I am sure that the approach and answer are correct. If you have any further questions or concerns, please let me know.