The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is ap
ID: 3239921 • Letter: T
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
1000 and 1500 chocolate chips, inclusive?
(b) What is the probability that a randomly selected bag contains fewer than
1000 chocolate chips?
(c) What proportion of bags contains more than 1175 chocolate chips?
(d) What is the percentile rank of a bag that contains 1000 chocolate chips?
Explanation / Answer
Mean = 1252
SD = 129
z = (x –Mean)/SD
Question a)
P (1000 <= x <= 1500)
z1 = (1000 -1252)/129
= -1.95
Z2 = (1500 -1252)/129
= 1.92
P (-1.95 < z < 1.92)
= P (z < 1.92) – P (z < -1.95)
By using normal table we get
= 0.9726 – 0.0256
= 0.9470
Answer 0.9470
Question b)
P ( x < 1000 )
= P ( z < -1.95)
By using Normal Table we get,
= 0.0256
Answer: 0.0256
Question c)
P (x > 1175)
z = (1175 -1252)/129
= -0.6
P (z>-0.6) = 1 – P (z<-0.6)
By using normal table we get,
= 1 - 0.2743
= 0.7257
Answer: 0.7257
Question d)
P (x < 1000 ) = 0.0256
~ 0.03
3rd percentiles
Answer: 3rd percentiles