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 1100 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?
(a) The probability that a randomly selected bag contains between 1000 and 1500 chocolate chips, inclusive, is
(Round to four decimal places as needed.)

Answer 1

Using the TI-83, 83+, 84, 84+ Calculator to calculate these probabilities

Go to 2nd DISTR, and select item 2: normalcdf

The syntax is: normalcdf (lower bound, upper bound, mean, standard deviation)

a) P(1100 <= X <= 1500)

= normalcdf(1100, 1500, 1252, 129)

= 0.8534

b) P(X < 1125)

= normalcdf(-1E99, 1125, 1252, 129)

= 0.1624

c) P(X > 1200)

= normalcdf(1200, 1E99, 1252, 129)

= 0.6566 = 65.66%

d) P(X < 1000)

= normalcdf(-1E99, 1000, 1252, 129)

= 0.0254 = approx 3rd percentile