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The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 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 1000 chocolate chips?

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 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 1000 chocolate chips?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Understanding Normal Distribution of Chocolate Chips in Cookie Bags** The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed. The mean is 1252 chips, and the standard deviation is 129 chips. This exercise explores different probabilities related to this distribution. ### Questions: **(a)** What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive? - To find this probability, calculate the area under the normal curve between the given chip counts. Use a standard normal distribution table or a calculator to determine the probability. (Round to four decimal places as needed.) **(b)** What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips? - This requires finding the area to the left of 1000 on the normal distribution curve. Use z-scores and normal distribution tables to find this probability. (Round to four decimal places as needed.) **(c)** What proportion of bags contains more than 1225 chocolate chips? - You need to find the area to the right of 1225 on the normal curve, which represents the proportion of bags with more than this number of chips. (Round to four decimal places as needed.) **(d)** What is the percentile rank of a bag that contains 1425 chocolate chips? - The percentile rank indicates the percentage of data points below a given value (1425 chips, in this case) in a distribution. Use z-scores to find this position on the normal curve and express it as a percentile. (Round to the nearest integer as needed.) Use these calculations to deepen your understanding of normal distribution and its applications in real-world scenarios, such as quality control in food production.
Transcribed Image Text:**Understanding Normal Distribution of Chocolate Chips in Cookie Bags** The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed. The mean is 1252 chips, and the standard deviation is 129 chips. This exercise explores different probabilities related to this distribution. ### Questions: **(a)** What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive? - To find this probability, calculate the area under the normal curve between the given chip counts. Use a standard normal distribution table or a calculator to determine the probability. (Round to four decimal places as needed.) **(b)** What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips? - This requires finding the area to the left of 1000 on the normal distribution curve. Use z-scores and normal distribution tables to find this probability. (Round to four decimal places as needed.) **(c)** What proportion of bags contains more than 1225 chocolate chips? - You need to find the area to the right of 1225 on the normal curve, which represents the proportion of bags with more than this number of chips. (Round to four decimal places as needed.) **(d)** What is the percentile rank of a bag that contains 1425 chocolate chips? - The percentile rank indicates the percentage of data points below a given value (1425 chips, in this case) in a distribution. Use z-scores to find this position on the normal curve and express it as a percentile. (Round to the nearest integer as needed.) Use these calculations to deepen your understanding of normal distribution and its applications in real-world scenarios, such as quality control in food production.
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