7.2.39 The number of chocolate chips in an 18-ounce bag of chocolate chip cookie

Question

7.2.39 The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips (a) What is the probability that a randomly selected bag contains between 1000 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1050 chocolate chips? (c) What proportion of bags contains more than 1225 chocolate chips? (d) What is the percentile rank of a bag that contains 1050 chocolate chips?

Explanation / Answer

Mean is 1252 and s is 129

z is given as (x-mean)/s

a) P(1000<x<1500)=P((1000-1252)/129<z<(1500-1252)/129)=P(-1.95<z<1.92) or P(z<1.92)-P(z<-1.95) or P(z<1.92)-(1-P(z<1.95)) , from normal distribution table gives 0.9726-(1-0.9744)=0.947

b) P(x<1050)=P(z<(1050-1252)/129)=P(z<-1.57) , from table it is 0.0582

c) P(x>1225)=P(z>(1225-1252)/129)=P(z>-0.21) or P(z<0.21) =0.5832

d) P(x<1050)=P(z<(1050-1252)/129)=P(z<-1.57) =0.0582 or 5.82 percentile

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.