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 undenweight? [ 9) 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 wi-w2017 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? [
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 undenweight? [ 9) 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 wi-w2017 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? [
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
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?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON