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 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 1425 chocolate chips?

Question

21-06-2019
Mathematics

contestada

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 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 1425 chocolate chips?

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88op 88op · Answer 1 · 2022-06-24T17:02:06+02:00

The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

Probability

The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

The probability exists a branch of mathematics that deals with calculating the likelihood of a given event's happening, which is defined as a number between 1 and 0. An event with a probability of 1 can be regarded as a certainty.

Utilizing the TI-83, 83+, 84, 84+ Calculator to estimate 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

To learn more about Probability refer to:

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