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
