Question

the number of chocolate chips in an 28 once bag of chocolate chips is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive, is

Answer 1

The probability is about 85.29%.

To do this, you need to first find the z-score on each end of the interval. Then, you can subtract the percents to find the percent in the middle.

Lower:
(1000 - 1252) / 129 = -1.18 which gives a probability of 11.9%

Upper:
(1500 - 1252) / 129 = 1.92 which gives a probability of 97.19%

97.19 - 11.9 = 85.29

Answer 2

The probability is 0.8536.

Z-scores are calculated using the formula 

z = (X - μ)/σ

For the lower limit we have
z = (1100-1252)/129 = -1.18

For the upper limit we have
z = (1500-1252)/129 = 1.92

Using a z-table (http://www.z-table.com) we see that the area to the left of the lower limit, less than that, is 0.1190.  The area to the left of the upper limit, less than that, is 0.9726.  The area between them is found by subtracting:

0.9726 - 0.1190 = 0.8536