Probability and Statistics for Engineers and Scientists
9th Edition
ISBN: 9780321629111
Author: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye
Publisher: Prentice Hall
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Chapter 3.4, Problem 79RE
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A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts?
1. Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
2. Compute the probability of a value greater than 55.0.
Use the same formula, x=55 and subtract the answer from 1.
3. Compute the probability of a value between 52.0 and 55.0.
(The question requires finding probability value between 52 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 52, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the…
If a uniform distribution is defined over the interval from 6 to 10, then answer the followings:
What is the mean of this uniform distribution?
Show that the probability of any value between 6 and 10 is equal to 1.0
Find the probability of a value more than 7.
Find the probability of a value between 7 and 9.
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be:
More than $27?
Less than or equal to $24?
The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches.
What is the mean amount of rainfall for the month?
What is the probability of less than an inch of rain for the month?
What is the probability of exactly 1.00 inch of rain?
What is the probability of more than 1.50 inches of rain for the month?
The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…
Client
1
Weight before
diet (pounds)
Weight after
diet (pounds)
128
120
2
131
123
3
140
141
4
178
170
5
121
118
6
136
136
7
118
121
8
136
127
Chapter 3 Solutions
Probability and Statistics for Engineers and Scientists
Ch. 3.3 - Classify the following random variables as...Ch. 3.3 - An overseas shipment of 5 foreign automobiles...Ch. 3.3 - Let W be a random variable giving the number of...Ch. 3.3 - A coin is flipped until 3 heads in succession...Ch. 3.3 - Determine the value c so that each of the...Ch. 3.3 - Prob. 6ECh. 3.3 - The total number of hours, measured in units of100...Ch. 3.3 - Find the probability distribution of the random...Ch. 3.3 - Prob. 9ECh. 3.3 - Find a formula for the probability distribution of...
Ch. 3.3 - A shipment of 7 television sets contains 2...Ch. 3.3 - An investment firm offers its customers municipal...Ch. 3.3 - The probability distribution of X, the number of...Ch. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Construct a graph of the cumulative distribution...Ch. 3.3 - A continuous random variable X that can assume...Ch. 3.3 - A continuous random variable X that can assume...Ch. 3.3 - For the density function of Exercise 3.17, find...Ch. 3.3 - For the density function of Exercise 3.18, find...Ch. 3.3 - Consider the density function
Evaluate k.
Find...Ch. 3.3 - Three cards are drawn in succession from a deck...Ch. 3.3 - Prob. 23ECh. 3.3 - Find the probability distribution for the number...Ch. 3.3 - From a box containing 4 dimes and 2 nickels, 3...Ch. 3.3 - From a box containing 4 black balls and 2 green...Ch. 3.3 - The time to failure in hours of an important piece...Ch. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Measurements of scientific systems are always...Ch. 3.3 - Based on extensive testing, it is determined by...Ch. 3.3 - Prob. 32ECh. 3.3 - Suppose a certain type of small data processing...Ch. 3.3 - Magnetron tubes are produced on an automated...Ch. 3.3 - Suppose it is known from large amounts of...Ch. 3.3 - On a laboratory assignment, if the equipment is...Ch. 3.4 - Prob. 37ECh. 3.4 - If the joint probability distribution of X and Y...Ch. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Let X and Y denote the lengths of life, in years,...Ch. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Let X denote the diameter of an armored electric...Ch. 3.4 - Referring to Exercise 3.38, find
the marginal...Ch. 3.4 - The amount of kerosene, in thousands of liters, in...Ch. 3.4 - Referring to Exercise 3.39, find
f(y|2) for all...Ch. 3.4 - Let X denote the number of times a certain...Ch. 3.4 - Suppose that X and Y have the following joint...Ch. 3.4 - Prob. 51ECh. 3.4 - A coin is tossed twice. Let Z denote the number of...Ch. 3.4 - Given the joint density function
find P(1< Y < 3...Ch. 3.4 - Determine whether the two random variables of...Ch. 3.4 - Determine whether the two random variables of...Ch. 3.4 - The joint density function of the random variables...Ch. 3.4 - Let X, Y, and Z have the joint probability density...Ch. 3.4 - Determine whether the two random variables of...Ch. 3.4 - Prob. 59ECh. 3.4 - The joint probability density function of the...Ch. 3.4 - Prob. 61RECh. 3.4 - Prob. 62RECh. 3.4 - Prob. 63RECh. 3.4 - Prob. 64RECh. 3.4 - Prob. 65RECh. 3.4 - Prob. 66RECh. 3.4 - Prob. 67RECh. 3.4 - Prob. 68RECh. 3.4 - Prob. 69RECh. 3.4 - Prob. 70RECh. 3.4 - Prob. 71RECh. 3.4 - Prob. 72RECh. 3.4 - Prob. 73RECh. 3.4 - Prob. 74RECh. 3.4 - A chemical system that results from a chemical...Ch. 3.4 - Consider the situation of Review Exercise 3.75....Ch. 3.4 - Prob. 77RECh. 3.4 - Prob. 78RECh. 3.4 - Prob. 79RECh. 3.4 - Prob. 80RE
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- Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?arrow_forwardIn order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forward
- Problem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…arrow_forwardPls help asaparrow_forwardSolve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forward
- ged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).arrow_forwardAn article in Business Week discussed the large spread between the federal funds rate and the average credit card rate. The table below is a frequency distribution of the credit card rate charged by the top 100 issuers. Credit Card Rates Credit Card Rate Frequency 18% -23% 19 17% -17.9% 16 16% -16.9% 31 15% -15.9% 26 14% -14.9% Copy Data 8 Step 1 of 2: Calculate the average credit card rate charged by the top 100 issuers based on the frequency distribution. Round your answer to two decimal places.arrow_forwardPlease could you check my answersarrow_forward
- Let Y₁, Y2,, Yy be random variables from an Exponential distribution with unknown mean 0. Let Ô be the maximum likelihood estimates for 0. The probability density function of y; is given by P(Yi; 0) = 0, yi≥ 0. The maximum likelihood estimate is given as follows: Select one: = n Σ19 1 Σ19 n-1 Σ19: n² Σ1arrow_forwardPlease could you help me answer parts d and e. Thanksarrow_forwardWhen fitting the model E[Y] = Bo+B1x1,i + B2x2; to a set of n = 25 observations, the following results were obtained using the general linear model notation: and 25 219 10232 551 XTX = 219 10232 3055 133899 133899 6725688, XTY 7361 337051 (XX)-- 0.1132 -0.0044 -0.00008 -0.0044 0.0027 -0.00004 -0.00008 -0.00004 0.00000129, Construct a multiple linear regression model Yin terms of the explanatory variables 1,i, x2,i- a) What is the value of the least squares estimate of the regression coefficient for 1,+? Give your answer correct to 3 decimal places. B1 b) Given that SSR = 5550, and SST=5784. Calculate the value of the MSg correct to 2 decimal places. c) What is the F statistics for this model correct to 2 decimal places?arrow_forward
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