The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 12521252 and standard deviation 129129 chips. (a) what is the probability that a randomly selected bag contains between 11001100 and 14001400 chocolate chips? (b) what is the probability that a randomly selected bag contains fewer than 10001000 chocolate chips? (c) what proportion of bags contains more than 12001200 chocolate chips? (d) what is the percentile rank of a bag that contains 10501050 chocolate chips?

The z-score is given by the formula:

z = (x-μ) / σ

μ=1252

σ=129

The answer to the questions given will be as follows:

a] what is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips?

z = (1400-1252) / 129

z=1.15625

P (x ≤ 1400) = 0.8770

z = (1100-1252) / 129

z=0.1190

P (X ≤1100) = 0.1190

the answer will be:

P (1100 ≤x≤1400) = 0.8770-0.1190=0.758

b] what is the probability that a randomly selected bag contains fewer than 1000 chocolate chips?

z = (1000-1252) / 129=-1.954

P (X≤1000) = 0.0256

c] what proportion of bags contains more than 1200 chocolate chips?

z = (1200-1252) / 129

z=-0.4031

P (X ≥1200) = 1-P (X ≤1200) = 1-0.4031=0.5969