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a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces?

a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces?

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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In this problem we look at bags of potato chips. There are three weights we consider. Let us call them Chip 1, Chip 2 and Chip 3. It is known that weights of potato chip bags are normally distributed. The weight of a Chip 1 bag has a mean weight of 8.05 ounces with a standard deviation 0.5 ounces, the weight of a Chip 2 bag has a mean weight of 10.5 ounces with a standard deviation 1.1 ounces, and the weight of a Chip 3 bag has a mean weight of 16 ounces with a standard deviation 1.7 ounces. Suppose we randomly select one Chip 1 bag, one Chip 2 bag and one Chip 3 bag. Let X = the total weight of the three bags selected. (Note: randomly selected means independent also.) a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces? d) What is the probability that X is between 33.03 and 36.10 ounces? e) If we pick a value k such that the probability that X > k equals .10 then calculate k? f) The chips are considered illegally underweight if the total weight X, is less than 32 ounces. What is the probability of the chips being considered underweight? g) We carry out the above chip weighing experiment 3 times. What is the probability that all 3 times, the weight X is < 32 ounces? h) We randomly select 2 Chip 1 bags. Call their weights w1 and w2. What is the probability that w1 - w2 > .01? i) What is the probability that the Chip 1 weight, the Chip 2 weight, and the Chip 3 weights are all greater than their expected values?
Transcribed Image Text:In this problem we look at bags of potato chips. There are three weights we consider. Let us call them Chip 1, Chip 2 and Chip 3. It is known that weights of potato chip bags are normally distributed. The weight of a Chip 1 bag has a mean weight of 8.05 ounces with a standard deviation 0.5 ounces, the weight of a Chip 2 bag has a mean weight of 10.5 ounces with a standard deviation 1.1 ounces, and the weight of a Chip 3 bag has a mean weight of 16 ounces with a standard deviation 1.7 ounces. Suppose we randomly select one Chip 1 bag, one Chip 2 bag and one Chip 3 bag. Let X = the total weight of the three bags selected. (Note: randomly selected means independent also.) a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces? d) What is the probability that X is between 33.03 and 36.10 ounces? e) If we pick a value k such that the probability that X > k equals .10 then calculate k? f) The chips are considered illegally underweight if the total weight X, is less than 32 ounces. What is the probability of the chips being considered underweight? g) We carry out the above chip weighing experiment 3 times. What is the probability that all 3 times, the weight X is < 32 ounces? h) We randomly select 2 Chip 1 bags. Call their weights w1 and w2. What is the probability that w1 - w2 > .01? i) What is the probability that the Chip 1 weight, the Chip 2 weight, and the Chip 3 weights are all greater than their expected values?
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In this problem we look at bags of potato chips. There are three weights we consider. Let us call them Chip 1, Chip 2 and Chip 3. It is known that weights of potato chip bags are normally distributed. The weight of a Chip 1 bag has a mean weight of 8.05 ounces with a standard deviation 0.5 ounces, the weight of a Chip 2 bag has a mean weight of 10.5 ounces with a standard deviation 1.1 ounces, and the weight of a Chip 3 bag has a mean weight of 16 ounces with a standard deviation 1.7 ounces. Suppose we randomly select one Chip 1 bag, one Chip 2 bag and one Chip 3 bag. Let X = the total weight of the three bags selected. (Note: randomly selected means independent also.) a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces? d) What is the probability that X is between 33.03 and 36.10 ounces? e) If we pick a value k such that the probability that X > k equals .10 then calculate k? f) The chips are considered illegally underweight if the total weight X, is less than 32 ounces. What is the probability of the chips being considered underweight? g) We carry out the above chip weighing experiment 3 times. What is the probability that all 3 times, the weight X is < 32 ounces? h) We randomly select 2 Chip 1 bags. Call their weights w1 and w2. What is the probability that w1 - w2 > .01? i) What is the probability that the Chip 1 weight, the Chip 2 weight, and the Chip 3 weights are all greater than their expected values?
Transcribed Image Text:In this problem we look at bags of potato chips. There are three weights we consider. Let us call them Chip 1, Chip 2 and Chip 3. It is known that weights of potato chip bags are normally distributed. The weight of a Chip 1 bag has a mean weight of 8.05 ounces with a standard deviation 0.5 ounces, the weight of a Chip 2 bag has a mean weight of 10.5 ounces with a standard deviation 1.1 ounces, and the weight of a Chip 3 bag has a mean weight of 16 ounces with a standard deviation 1.7 ounces. Suppose we randomly select one Chip 1 bag, one Chip 2 bag and one Chip 3 bag. Let X = the total weight of the three bags selected. (Note: randomly selected means independent also.) a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces? d) What is the probability that X is between 33.03 and 36.10 ounces? e) If we pick a value k such that the probability that X > k equals .10 then calculate k? f) The chips are considered illegally underweight if the total weight X, is less than 32 ounces. What is the probability of the chips being considered underweight? g) We carry out the above chip weighing experiment 3 times. What is the probability that all 3 times, the weight X is < 32 ounces? h) We randomly select 2 Chip 1 bags. Call their weights w1 and w2. What is the probability that w1 - w2 > .01? i) What is the probability that the Chip 1 weight, the Chip 2 weight, and the Chip 3 weights are all greater than their expected values?
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i need perfect answer for d e f 

In this problem we look at bags of potato chips. There are three weights we consider. Let us call them Chip 1, Chip 2 and Chip 3. It is known that weights of potato chip bags are normally distributed. The weight of a Chip 1 bag has a mean weight of 8.05 ounces with a standard deviation 0.5 ounces, the weight of a Chip 2 bag has a mean weight of 10.5 ounces with a standard deviation 1.1 ounces, and the weight of a Chip 3 bag has a mean weight of 16 ounces with a standard deviation 1.7 ounces. Suppose we randomly select one Chip 1 bag, one Chip 2 bag and one Chip 3 bag. Let X = the total weight of the three bags selected. (Note: randomly selected means independent also.) a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces? d) What is the probability that X is between 33.03 and 36.10 ounces? e) If we pick a value k such that the probability that X > k equals .10 then calculate k? f) The chips are considered illegally underweight if the total weight X, is less than 32 ounces. What is the probability of the chips being considered underweight? g) We carry out the above chip weighing experiment 3 times. What is the probability that all 3 times, the weight X is < 32 ounces? h) We randomly select 2 Chip 1 bags. Call their weights w1 and w2. What is the probability that w1 - w2 > .01? i) What is the probability that the Chip 1 weight, the Chip 2 weight, and the Chip 3 weights are all greater than their expected values?
Transcribed Image Text:In this problem we look at bags of potato chips. There are three weights we consider. Let us call them Chip 1, Chip 2 and Chip 3. It is known that weights of potato chip bags are normally distributed. The weight of a Chip 1 bag has a mean weight of 8.05 ounces with a standard deviation 0.5 ounces, the weight of a Chip 2 bag has a mean weight of 10.5 ounces with a standard deviation 1.1 ounces, and the weight of a Chip 3 bag has a mean weight of 16 ounces with a standard deviation 1.7 ounces. Suppose we randomly select one Chip 1 bag, one Chip 2 bag and one Chip 3 bag. Let X = the total weight of the three bags selected. (Note: randomly selected means independent also.) a) Calculate the expected value of X in ounces. b) Calculate the standard deviation of X in ounces. c) What is the probability that X is more than 37 ounces? d) What is the probability that X is between 33.03 and 36.10 ounces? e) If we pick a value k such that the probability that X > k equals .10 then calculate k? f) The chips are considered illegally underweight if the total weight X, is less than 32 ounces. What is the probability of the chips being considered underweight? g) We carry out the above chip weighing experiment 3 times. What is the probability that all 3 times, the weight X is < 32 ounces? h) We randomly select 2 Chip 1 bags. Call their weights w1 and w2. What is the probability that w1 - w2 > .01? i) What is the probability that the Chip 1 weight, the Chip 2 weight, and the Chip 3 weights are all greater than their expected values?
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