Mathematical Statistics and Data Analysis
3rd Edition
ISBN: 9781111793715
Author: John A. Rice
Publisher: Cengage Learning
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Chapter 1.8, Problem 47P
a.
To determine
Find the
b.
To determine
Find the probability that a red ball is drawn from urn A if a red ball is drawn from urn B.
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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 1 Solutions
Mathematical Statistics and Data Analysis
Ch. 1.8 - Prob. 1PCh. 1.8 - Prob. 2PCh. 1.8 - Prob. 3PCh. 1.8 - Prob. 4PCh. 1.8 - Prob. 5PCh. 1.8 - Prob. 6PCh. 1.8 - Prob. 7PCh. 1.8 - Prob. 8PCh. 1.8 - Prob. 9PCh. 1.8 - Prob. 10P
Ch. 1.8 - Prob. 11PCh. 1.8 - Prob. 12PCh. 1.8 - Prob. 13PCh. 1.8 - Prob. 14PCh. 1.8 - Prob. 15PCh. 1.8 - Prob. 16PCh. 1.8 - Prob. 17PCh. 1.8 - Prob. 18PCh. 1.8 - Prob. 19PCh. 1.8 - Prob. 20PCh. 1.8 - Prob. 21PCh. 1.8 - Prob. 22PCh. 1.8 - Prob. 23PCh. 1.8 - Prob. 24PCh. 1.8 - Prob. 25PCh. 1.8 - Prob. 26PCh. 1.8 - Prob. 27PCh. 1.8 - Prob. 28PCh. 1.8 - Prob. 29PCh. 1.8 - Prob. 30PCh. 1.8 - Prob. 31PCh. 1.8 - Prob. 32PCh. 1.8 - Prob. 33PCh. 1.8 - Prob. 34PCh. 1.8 - Prob. 35PCh. 1.8 - Prob. 36PCh. 1.8 - Prob. 37PCh. 1.8 - Prob. 38PCh. 1.8 - Prob. 39PCh. 1.8 - Prob. 40PCh. 1.8 - Prob. 41PCh. 1.8 - Prob. 42PCh. 1.8 - Prob. 43PCh. 1.8 - Prob. 44PCh. 1.8 - Prob. 45PCh. 1.8 - Prob. 46PCh. 1.8 - Prob. 47PCh. 1.8 - Prob. 48PCh. 1.8 - Prob. 49PCh. 1.8 - Prob. 50PCh. 1.8 - Prob. 51PCh. 1.8 - Prob. 52PCh. 1.8 - Prob. 53PCh. 1.8 - Prob. 54PCh. 1.8 - Prob. 55PCh. 1.8 - Prob. 56PCh. 1.8 - Prob. 57PCh. 1.8 - Prob. 59PCh. 1.8 - Prob. 60PCh. 1.8 - Prob. 61PCh. 1.8 - Prob. 62PCh. 1.8 - Prob. 63PCh. 1.8 - Prob. 64PCh. 1.8 - Prob. 65PCh. 1.8 - Prob. 66PCh. 1.8 - Prob. 67PCh. 1.8 - Prob. 68PCh. 1.8 - Prob. 69PCh. 1.8 - Prob. 70PCh. 1.8 - Prob. 71PCh. 1.8 - Prob. 72PCh. 1.8 - Prob. 73PCh. 1.8 - Prob. 74PCh. 1.8 - Prob. 75PCh. 1.8 - Prob. 77PCh. 1.8 - Prob. 78PCh. 1.8 - Prob. 79PCh. 1.8 - Prob. 80P
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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
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- 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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