The number of chocolate chips in an 18ounce bag of chocolate

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 1400 chocolate chips, inclusive?

(b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips?

(c) What proportion of bags contains more than 1225 chocolate chips?

(d) What is the percentile rank of a bag that contains 1025 chocolate chips?

Solution

A) P(1000 < x < 1400) = ?

z = (1000 - 1252)/(129) = -1.9534

z = (1400 - 1252)/(129) = 1.1472


P(1000 < x < 1400) =

P(-1.9534 < z < 1.1472)

= 0.849 = 0.85

B)z = (x - µ)/
= (1125 - 1252)/129 = -0.984

We want to know the probability that the bag will have FEWER than 1125 chips so we look up the z value of -0.984 and find that the probability of finding a value BELOW that z is:

0.1626= 16.26%

C) z = (x - µ)/
= (1225 - 1252)/129 = -0.2093

The value from the table at z = -0.2093 is 0.417107. This gives us the probability of finding a value BELOW 1225, but we want the probability of selecting a value GREATER than 1225. So we\'ll use the Complement Rule to find the probability of selecting a bag with MORE than 1225 chips:

1 - 0.417107 = 0.5829 = 58.29%