Question

The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. ​(a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate​ chips, inclusive? ​(b) What is the probability that a randomly selected bag contains fewer than 1025 chocolate​ chips? ​(c) What proportion of bags contains more than 1200 chocolate​ chips? ​(d) What is the percentile rank of a bag that contains 1050 chocolate​ chips?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	1252
std deviation   =σ=	129.0000

probability =

P(1100<X<1500)

=

P(-1.18<Z<1.92)=

0.9726-0.1190=

0.8536

b)

probability that a randomly selected bag contains fewer than 1025 chocolate​ chips :

probability =

P(X<1025)

=

P(Z<-1.76)=

0.0392

c)

proportion of bags contains more than 1200 chocolate​ chips :

probability =

P(X>1200)

=

P(Z>-0.4)=

1-P(Z<-0.4)=

1-0.3446=

0.6554

d)

probability =

P(X<1050)

=

P(Z<-1.57)=

0.0582 ~5.82 th percentile