INTRO.TO MATHEMATICAL STAT...-STD.SOLN.
6th Edition
ISBN: 9780134114262
Author: LARSEN
Publisher: PEARSON
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Chapter 3.2, Problem 19Q
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To find: The
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Microsoft Excel snapshot for random sampling: Also note the formula used for the last
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x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
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No.
States
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ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
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E
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G
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No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
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2 ALASKA
0.4493186 OKLAHOMA
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3 ARIZONA
0.707914 KANSAS
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4 ARKANSAS 0.4831379 NORTH DAKOTA
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5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
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6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
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8 DELAWARE 0.5783029 MISSOURI
525
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INDIANA
MARYLAND
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Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined.
1.What percent of the refunds are more than $3,500?
2. What percent of the refunds are more than $3500 but less than $3579?
3. What percent of the refunds are more than $3325 but less than $3579?
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…
Chapter 3 Solutions
INTRO.TO MATHEMATICAL STAT...-STD.SOLN.
Ch. 3.2 - An investment analyst has tracked a certain...Ch. 3.2 - In a nuclear reactor, the fission process is...Ch. 3.2 - In 2009 a donor who insisted on anonymity gave...Ch. 3.2 - An entrepreneur owns six corporations, each with...Ch. 3.2 - The probability is 0.10 that ball bearings in a...Ch. 3.2 - Suppose that since the early 1950s some...Ch. 3.2 - Doomsday Airlines (Come Take the Flight of Your...Ch. 3.2 - Two lighting systems are being proposed for an...Ch. 3.2 - The great English diarist Samuel Pepys asked his...Ch. 3.2 - The gunner on a small assault boat fires six...
Ch. 3.2 - If a family has four children, is it more likely...Ch. 3.2 - Experience has shown that only 13 of all patients...Ch. 3.2 - Transportation to school for a rural countys...Ch. 3.2 - The captain of a Navy gunboat orders a volley of...Ch. 3.2 - A computer has generated seven random numbers over...Ch. 3.2 - Listed in the following table is the length...Ch. 3.2 - Redo Example 3.2.4 assuming n=12 and p=0.3.Ch. 3.2 - Prob. 18QCh. 3.2 - Prob. 19QCh. 3.2 - A corporate board contains twelve members. The...Ch. 3.2 - One of the popular tourist attractions in Alaska...Ch. 3.2 - A city has 4050 children under the age of ten,...Ch. 3.2 - Country A inadvertently launches ten guided...Ch. 3.2 - Anne is studying for a history exam covering the...Ch. 3.2 - Each year a college awards five merit-based...Ch. 3.2 - Keno is a casino game in which the player has a...Ch. 3.2 - A display case contains thirty-five gems, of which...Ch. 3.2 - Consider an urn with r red balls and w white...Ch. 3.2 - Prob. 29QCh. 3.2 - Prob. 30QCh. 3.2 - Prob. 31QCh. 3.2 - Prob. 32QCh. 3.2 - Prob. 33QCh. 3.2 - Some nomadic tribes, when faced with a...Ch. 3.2 - Suppose a population contains n1 objects of one...Ch. 3.2 - Prob. 36QCh. 3.3 - Prob. 1QCh. 3.3 - Repeat Question 3.3.1 for the case where the two...Ch. 3.3 - Suppose a fair die is tossed three times. Let X be...Ch. 3.3 - Suppose a fair die is tossed three times. Let X be...Ch. 3.3 - A fair coin is tossed three times. Let X be the...Ch. 3.3 - Suppose die one has spots 1, 2, 2, 3, 3, 4 and die...Ch. 3.3 - Suppose a particle moves along the x-axis...Ch. 3.3 - How would the pdf asked for in Question 3.3.7 be...Ch. 3.3 - Suppose that five people, including you and a...Ch. 3.3 - Prob. 10QCh. 3.3 - Prob. 11QCh. 3.3 - Prob. 12QCh. 3.3 - A fair die is rolled four times. Let the random...Ch. 3.3 - At the points x=0,1,...,6, the cdf for the...Ch. 3.3 - Find the pdf for the infinite-valued discrete...Ch. 3.3 - Recall the game of Fantasy Five from Example...Ch. 3.4 - Suppose fY(y)=4y3,0y1. Find P(0Y12).Ch. 3.4 - For the random variable Y with pdf...Ch. 3.4 - Let fY(y)=23y2,1y1. Find P(|Y12|14). Draw a graph...Ch. 3.4 - For persons infected with a certain form of...Ch. 3.4 - For a high-risk driver, the time in days between...Ch. 3.4 - Let n be a positive integer. Show that...Ch. 3.4 - Find the cdf for the random variable Y given in...Ch. 3.4 - If Y is an exponential random variable,...Ch. 3.4 - If the pdf for Y is fY(y)={0,|y|11|y|,|y|1 find...Ch. 3.4 - Prob. 10QCh. 3.4 - Prob. 11QCh. 3.4 - Prob. 12QCh. 3.4 - Prob. 13QCh. 3.4 - Prob. 14QCh. 3.4 - The logistic curve F(y)=11+ey,y, can represent a...Ch. 3.4 - Prob. 16QCh. 3.4 - Prob. 17QCh. 3.4 - Let Y be a random variable denoting the age at...Ch. 3.5 - Recall the game of Keno described in Question...Ch. 3.5 - The roulette wheels in Monte Carlo typically have...Ch. 3.5 - The pdf describing the daily profit, X, earned by...Ch. 3.5 - In the game of redball, two drawings are made...Ch. 3.5 - Suppose a life insurance company sells a $50,000,...Ch. 3.5 - A manufacturer has one hundred memory chips in...Ch. 3.5 - Records show that 642 new students have just...Ch. 3.5 - Prob. 8QCh. 3.5 - Recall Question 3.4.4, where the length of time Y...Ch. 3.5 - Let the random variable Y have the uniform...Ch. 3.5 - Show that the expected value associated with the...Ch. 3.5 - Show that fY(y)=1y2,y1 is a valid pdf but that Y...Ch. 3.5 - Based on recent experience, ten-year-old passenger...Ch. 3.5 - Prob. 14QCh. 3.5 - A city has 74,806 registered automobiles. Each is...Ch. 3.5 - Regulators have found that twenty-three of the...Ch. 3.5 - An urn contains four chips numbered 1 through 4....Ch. 3.5 - A fair coin is tossed three times. Let the random...Ch. 3.5 - Prob. 19QCh. 3.5 - For the St. Petersburg problem (Example 3.5.5),...Ch. 3.5 - Prob. 21QCh. 3.5 - Prob. 22QCh. 3.5 - Suppose that two evenly matched teams are playing...Ch. 3.5 - An urn contains one white chip and one black chip....Ch. 3.5 - Prob. 25QCh. 3.5 - Prob. 26QCh. 3.5 - Find the median for each of the following pdfs:...Ch. 3.5 - Suppose X is a binomial random variable with n=10...Ch. 3.5 - A typical days production of a certain electronic...Ch. 3.5 - Let Y have probability density function...Ch. 3.5 - Prob. 31QCh. 3.5 - A box is to be constructed so that its height is...Ch. 3.5 - Prob. 33QCh. 3.5 - If Y has probability density function fY(y)=2y,0y1...Ch. 3.5 - Prob. 35QCh. 3.5 - Prob. 36QCh. 3.6 - Find Var(X) for the urn problem of Example 3.6.1...Ch. 3.6 - Find the variance of Y if...Ch. 3.6 - Ten equally qualified applicants, six men and four...Ch. 3.6 - A certain hospitalization policy pays a cash...Ch. 3.6 - Use Theorem 3.6.1 to find the variance of the...Ch. 3.6 - If fY(y)=2yk2,0yk for what value of k does...Ch. 3.6 - Calculate the standard deviation, , for the random...Ch. 3.6 - Consider the pdf defined by fY(y)=2y3,y1 Show that...Ch. 3.6 - Frankie and Johnny play the following game....Ch. 3.6 - Let Y be a random variable whose pdf is given by...Ch. 3.6 - Suppose that Y is an exponential random variable,...Ch. 3.6 - Suppose that Y is an exponential random variable...Ch. 3.6 - Let X be a random variable with finite mean ....Ch. 3.6 - Suppose the charge for repairing an automobile...Ch. 3.6 - If Y denotes a temperature recorded in degrees...Ch. 3.6 - Prob. 16QCh. 3.6 - Suppose U is a uniform random variable over [0,1]....Ch. 3.6 - Recovering small quantities of calcium in the...Ch. 3.6 - Let Y be a uniform random variable defined over...Ch. 3.6 - Find the coefficient of skewness for an...Ch. 3.6 - Calculate the coefficient of kurtosis for a...Ch. 3.6 - Suppose that W is a random variable for which...Ch. 3.6 - If Y=aX+b,a0, show that Y has the same...Ch. 3.6 - Let Y be the random variable of Question 3.4.6,...Ch. 3.6 - Prob. 25QCh. 3.7 - Prob. 1QCh. 3.7 - Prob. 2QCh. 3.7 - Prob. 3QCh. 3.7 - Find c if fX,Y(x,y)=cxy for X and Y defined over...Ch. 3.7 - Prob. 5QCh. 3.7 - Four cards are drawn from a standard poker deck....Ch. 3.7 - An advisor looks over the schedules of his fifty...Ch. 3.7 - Consider the experiment of tossing a fair coin...Ch. 3.7 - Suppose that two fair dice are tossed one time....Ch. 3.7 - Let X be the time in days between a car accident...Ch. 3.7 - Let X and Y have the joint pdf...Ch. 3.7 - A point is chosen at random from the interior of a...Ch. 3.7 - Find P(X2Y) if fX,Y(x,y)=x+y for X and Y each...Ch. 3.7 - Prob. 14QCh. 3.7 - A point is chosen at random from the interior of a...Ch. 3.7 - Prob. 16QCh. 3.7 - Find the marginal pdfs of X and Y for the joint...Ch. 3.7 - Prob. 18QCh. 3.7 - For each of the following joint pdfs, find fX(x)...Ch. 3.7 - For each of the following joint pdfs, find fX(x)...Ch. 3.7 - Prob. 21QCh. 3.7 - Prob. 22QCh. 3.7 - Prob. 23QCh. 3.7 - Prob. 24QCh. 3.7 - Consider the experiment of simultaneously tossing...Ch. 3.7 - Prob. 26QCh. 3.7 - For each of the following joint pdfs, find...Ch. 3.7 - Prob. 28QCh. 3.7 - Prob. 29QCh. 3.7 - Prob. 30QCh. 3.7 - Given that FX,Y(x,y)=k(4x2y2+5xy4),0x1,0y1, find...Ch. 3.7 - Prob. 32QCh. 3.7 - Prob. 33QCh. 3.7 - Prob. 34QCh. 3.7 - Prob. 35QCh. 3.7 - Prob. 36QCh. 3.7 - Prob. 37QCh. 3.7 - Prob. 38QCh. 3.7 - Prob. 39QCh. 3.7 - Suppose that each of two urns has four chips,...Ch. 3.7 - Let X and Y be random variables with joint pdf...Ch. 3.7 - Are the random variables X and Y independent if...Ch. 3.7 - Prob. 43QCh. 3.7 - Find the joint cdf of the independent random...Ch. 3.7 - Prob. 45QCh. 3.7 - Prob. 46QCh. 3.7 - Prob. 47QCh. 3.7 - Prob. 48QCh. 3.7 - Prob. 49QCh. 3.7 - Prob. 50QCh. 3.7 - Suppose that X1,X2,X3, and X4 are independent...Ch. 3.7 - Prob. 52QCh. 3.8 - Prob. 1QCh. 3.8 - Prob. 2QCh. 3.8 - Prob. 3QCh. 3.8 - Prob. 4QCh. 3.8 - Prob. 5QCh. 3.8 - Prob. 6QCh. 3.8 - Prob. 7QCh. 3.8 - Prob. 8QCh. 3.8 - Prob. 9QCh. 3.8 - Prob. 10QCh. 3.8 - Prob. 11QCh. 3.8 - Prob. 12QCh. 3.8 - Prob. 13QCh. 3.9 - Prob. 1QCh. 3.9 - Prob. 2QCh. 3.9 - Suppose that fX,Y(x,y)=23(x+2y),0x1,0y1 [recall...Ch. 3.9 - Marksmanship competition at a certain level...Ch. 3.9 - Suppose that Xi is a random variable for which...Ch. 3.9 - Prob. 6QCh. 3.9 - Prob. 7QCh. 3.9 - Suppose two fair dice are tossed. Find the...Ch. 3.9 - Prob. 9QCh. 3.9 - Suppose that X and Y are both uniformly...Ch. 3.9 - Prob. 11QCh. 3.9 - Prob. 12QCh. 3.9 - Prob. 13QCh. 3.9 - Prob. 14QCh. 3.9 - Prob. 15QCh. 3.9 - Let X and Y be random variables with...Ch. 3.9 - Suppose that fX,Y(x,y)=2e(x+y),0x,0y. Find...Ch. 3.9 - Prob. 18QCh. 3.9 - Prob. 19QCh. 3.9 - Let X be a binomial random variable based on n...Ch. 3.9 - Prob. 21QCh. 3.9 - Prob. 22QCh. 3.9 - Prob. 23QCh. 3.9 - A gambler plays n hands of poker. If he wins the...Ch. 3.10 - Suppose the length of time, in minutes, that you...Ch. 3.10 - A random sample of size n=6 is taken from the pdf...Ch. 3.10 - What is the probability that the larger of two...Ch. 3.10 - Prob. 4QCh. 3.10 - Prob. 5QCh. 3.10 - Let Y1,Y2,...,Yn be a random sample from the...Ch. 3.10 - Calculate P(0.6Y40.7) if a random sample of size 6...Ch. 3.10 - A random sample of size n=5 is drawn from the pdf...Ch. 3.10 - Prob. 9QCh. 3.10 - Suppose that n observations are chosen at random...Ch. 3.10 - In a certain large metropolitan area, the...Ch. 3.10 - Consider a system containing n components, where...Ch. 3.10 - Prob. 13QCh. 3.10 - Prob. 14QCh. 3.10 - Prob. 15QCh. 3.10 - Suppose a device has three independent components,...Ch. 3.11 - Prob. 1QCh. 3.11 - Suppose a die is rolled six times. Let X be the...Ch. 3.11 - Prob. 3QCh. 3.11 - Five cards are dealt from a standard poker deck....Ch. 3.11 - Given that two discrete random variables X and Y...Ch. 3.11 - Prob. 6QCh. 3.11 - Suppose X, Y, and Z have a trivariate distribution...Ch. 3.11 - Prob. 8QCh. 3.11 - Let X and Y be independent Poisson random...Ch. 3.11 - Prob. 10QCh. 3.11 - Prob. 11QCh. 3.11 - Prob. 12QCh. 3.11 - Prob. 13QCh. 3.11 - Prob. 14QCh. 3.11 - Prob. 15QCh. 3.11 - Prob. 16QCh. 3.11 - Prob. 17QCh. 3.11 - Prob. 18QCh. 3.11 - Prob. 19QCh. 3.11 - Prob. 20QCh. 3.11 - For continuous random variables X and Y, prove...Ch. 3.12 - Let X be a random variable with pdf pX(k)=1/n, for...Ch. 3.12 - Two chips are drawn at random and without...Ch. 3.12 - Prob. 3QCh. 3.12 - Find the moment-generating function for the...Ch. 3.12 - Which pdfs would have the following...Ch. 3.12 - Prob. 6QCh. 3.12 - The random variable X has a Poisson distribution...Ch. 3.12 - Prob. 8QCh. 3.12 - Prob. 9QCh. 3.12 - Find E(Y4) if Y is an exponential random variable...Ch. 3.12 - Prob. 11QCh. 3.12 - Prob. 12QCh. 3.12 - Prob. 13QCh. 3.12 - Prob. 14QCh. 3.12 - Prob. 15QCh. 3.12 - Find the variance of Y if MY(t)=e2t/(1t2).Ch. 3.12 - Prob. 17QCh. 3.12 - Let Y1,Y2, and Y3 be independent random variables,...Ch. 3.12 - Use Theorems 3.12.2 and 3.12.3 to determine which...Ch. 3.12 - Calculate P(X2) if MX(t)=(14+34et)5.Ch. 3.12 - Suppose that Y1,Y2,...,Yn is a random sample of...Ch. 3.12 - Suppose the moment-generating function for a...Ch. 3.12 - Suppose that X is a Poisson random variable, where...Ch. 3.12 - Prob. 24Q
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- 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…arrow_forwardClient 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 127arrow_forwardClient 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_forward
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