Question

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?

Answer 1

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