Finite Mathematics for the Managerial, Life, and Social Sciences
12th Edition
ISBN: 9781337405782
Author: Soo T. Tan
Publisher: Cengage Learning
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Chapter 8.4, Problem 62E
To determine
Whether the statement is true or false and the reason for it.
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Set up a free RStudio account at posit.cloud. At the start of your R session, you should enter the following commands.
set.seed(1)
e<-rnorm(n = 100,mean = 0,sd = 80)
x<-seq(1,100,1)
y<-10+15*x + e
Follow the examples in the Panopto Videos to use R to obtain the values requested below. (As always, if you round your answers, make sure you do so correctly and keep at least
three decimal places.)
(a) The smallest value of y =
(b) The largest value of y =
(c) The standard deviation of y =
(d) The mean of y =
(e) The median of y =
(f) The correlation between x and y =
:
(g) Using the variable e as data, the p-value for a test of Hoμ = 0 vs. HA μ0 is
3. (i) Using the definition of the line integral of a vector field, calculate the
line integral
L³
F.dy
of the vector field F: R² → R² given by
F(x, y) = (y, x),
and where the curve & is the unit semi-circle centred at the origin, located in
the upper half-plane and oriented in the anticlockwise direction.
Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9
in the Notes).
[20 Marks]
(ii) Calculate the same integral using Green's Theorem.
[10 Marks]
1. Evaluate the integral
↓ f(x, y)dxdy,
of function f R² →R over the domain DC R2, where:
f(x, y) = 2x + y
and D is the is the triangle with vertices (0, -1), (1,0) and (0,2).
Hint. Represent D in the form D = {(x, y) = R² : x = (a, b), g(x) < y < h(x)} for
some a
Chapter 8 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
Ch. 8.1 - What is a random variable? Give an example.Ch. 8.1 - Prob. 2CQCh. 8.1 - Prob. 3CQCh. 8.1 - Three balls are selected at random without...Ch. 8.1 - 2.A coin is tossed four times. Let the random...Ch. 8.1 - A die is rolled repeatedly until a 6 falls...Ch. 8.1 - Cards are selected one at a time without...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7E
Ch. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - In Exercises 7-12, give the range of values that...Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - In Exercises 13-16, determine whether the table...Ch. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - In Exercises 17-18, find conditions on the numbers...Ch. 8.1 - Prob. 19ECh. 8.1 - The probability distribution of the random...Ch. 8.1 - Prob. 21ECh. 8.1 - EXAMS An examination consisting of ten...Ch. 8.1 - Two dice are rolled. Let the random variable X...Ch. 8.1 - Prob. 24ECh. 8.1 - MONEY MARKET RATES The interest rates paid by 30...Ch. 8.1 - DISTRIBUTION OF FAMILIES BY SIZE The Public...Ch. 8.1 - WAITNG LINES The accompanying data were obtained...Ch. 8.1 - TELEVISION PILOTS After the private screening of a...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 1TECh. 8.1 - Prob. 2TECh. 8.1 - Prob. 3TECh. 8.1 - Prob. 4TECh. 8.1 - Prob. 5TECh. 8.1 - Prob. 6TECh. 8.1 - Prob. 7TECh. 8.1 - Prob. 8TECh. 8.1 - Prob. 9TECh. 8.1 - Prob. 10TECh. 8.2 - What is the expected value of a random variable?...Ch. 8.2 - Prob. 2CQCh. 8.2 - Prob. 3CQCh. 8.2 - Prob. 1ECh. 8.2 - Find the expected value of a random variable X...Ch. 8.2 - CALCULATING GPA During the first year at a...Ch. 8.2 - Prob. 4ECh. 8.2 - EXPECTED SALES On the basis of past experience,...Ch. 8.2 - CAFETERIA MILK CONSUMPTION Records kept by the...Ch. 8.2 - EXPECTED EARNINGS The daily earnings X of an...Ch. 8.2 - EXPECTED NUMBER OF DEFECTIVE PRODUCTS If a sample...Ch. 8.2 - EXPECTED NUMBER OF AUTO ACCIDENTS The numbers of...Ch. 8.2 - EXPECTED DEMAND FOR MAGAZINES The owner of a...Ch. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - EXPECTED VALUE OF A LOTTERY TICKET In a lottery,...Ch. 8.2 - LIFE INSURANCE PREMIUMS A man wishes to purchase a...Ch. 8.2 - Prob. 17ECh. 8.2 - LIFE INSURANCE PREMIUMS As a fringe benefit,...Ch. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - EXPECTED AUTO SALES OF A DEALERSHIP Roger Hunt...Ch. 8.2 - EXPECTED HOME SALES OF A REALTOR Sally Leonard, a...Ch. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - ODDS OF MAKING A SALE Carmen, a computer sales...Ch. 8.2 - Prob. 39ECh. 8.2 - ODDS OF WINNING A BOXING MATCH If a sports...Ch. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Wage Rates The frequency distribution of the...Ch. 8.2 - Prob. 45ECh. 8.2 - SAN FRANCISCO WEATHER The normal daily minimum...Ch. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - MINIMUM WAGE The minimum wage in the 13 states...Ch. 8.2 - Prob. 53ECh. 8.2 - In Exercises 53 and 54, determine whether the...Ch. 8.3 - a. What is the variance of a random variable X? b....Ch. 8.3 - Prob. 2CQCh. 8.3 - Prob. 1ECh. 8.3 - In Exercises 1-6, the probability distribution of...Ch. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - In Exercises 9 and 10, find the variance of the...Ch. 8.3 - Prob. 10ECh. 8.3 - An experiment consists of rolling an eight-sided...Ch. 8.3 - Happiness Score The happiness score, by...Ch. 8.3 - Prob. 13ECh. 8.3 - INVESTMENT ANALYSIS Paul Hunt is considering two...Ch. 8.3 - INVESTMENT ANALYSIS Rosa Walters is considering...Ch. 8.3 - The distribution of the number of chocolate chips...Ch. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - STUCK IN TRAFFIC The following table gives the...Ch. 8.3 - COST OF TAKING TIME OFF A survey was conducted of...Ch. 8.3 - Prob. 21ECh. 8.3 - NEW YORK STATE COURTS' TOTAL CASELOAD The...Ch. 8.3 - Prob. 23ECh. 8.3 - IDENTITY FRAUD The identity fraud rates in the...Ch. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Prob. 40ECh. 8.3 - A Probability distribution has mean of 42 and a...Ch. 8.3 - A Probability distribution has mean of 20 and a...Ch. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 1TECh. 8.3 - Prob. 2TECh. 8.3 - Prob. 3TECh. 8.3 - Prob. 4TECh. 8.3 - Prob. 5TECh. 8.3 - Prob. 6TECh. 8.3 - Prob. 7TECh. 8.3 - Prob. 8TECh. 8.4 - Suppose that you are given a Bernoulli experiment....Ch. 8.4 - Prob. 2CQCh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - In Exercises 1116, use the formula C(n,x)pxqnx to...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - A binomial experiment consists of five independent...Ch. 8.4 - FAMILY COMPOSITION Let the random variable X...Ch. 8.4 - Prob. 21ECh. 8.4 - SPORTS If the probability that a certain tennis...Ch. 8.4 - Prob. 23ECh. 8.4 - VOTERS In a certain congressional district. it is...Ch. 8.4 - Prob. 25ECh. 8.4 - AVAILABILITY OF CUSTOMER SERVTCE Mayco, a...Ch. 8.4 - RESTAURANT HEALTH CODE VIOLATIONS Suppose 30 of...Ch. 8.4 - Prob. 28ECh. 8.4 - EXAMS A psychology quiz consists of ten...Ch. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - MAKING FRIENDS In a survey of 2541 adults aged 18...Ch. 8.4 - EXAMS A biology quiz consists of eight...Ch. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.4 - CONSUMER PREFERENCES An advertisement for Brand A...Ch. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - BLOOD PRESSURE A study conducted in 2012...Ch. 8.4 - Prob. 40ECh. 8.4 - CREDIT SCORES In a survey of 1010 married adults,...Ch. 8.4 - WORKING WITH A SPOUSE In a survey of 1147 small...Ch. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - ROBOT RELIABILITY An automobile manufacturing...Ch. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Prob. 52ECh. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.4 - Prob. 55ECh. 8.4 - Prob. 56ECh. 8.4 - Prob. 57ECh. 8.4 - Prob. 58ECh. 8.4 - Prob. 59ECh. 8.4 - Prob. 60ECh. 8.4 - Prob. 61ECh. 8.4 - Prob. 62ECh. 8.5 - Consider the following normal curve with mean and...Ch. 8.5 - Prob. 2CQCh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - In Exercise 714, a make a sketch of the area under...Ch. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.6 - What does Theorem 1, page 532, allow us to do?Ch. 8.6 - Prob. 2CQCh. 8.6 - Medical Records The medical record of infant...Ch. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - IQsThe IQs of students at Wilson Elementary School...Ch. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - WARRANTIES The general manager of the service...Ch. 8.6 - Prob. 10ECh. 8.6 - GRADE DISTRIBUTION The score on a sociology...Ch. 8.6 - HIGHWAY SPEEDS The speeds in miles per hour of...Ch. 8.6 - In Exercise 13-24, use the appropriate normal...Ch. 8.6 - Prob. 14ECh. 8.6 - Prob. 15ECh. 8.6 - CHANCE OF MAKING A FREE THROW A basketball player...Ch. 8.6 - Prob. 17ECh. 8.6 - TELEMARKETING Jorge sells magazine subscription...Ch. 8.6 - Prob. 19ECh. 8.6 - Prob. 20ECh. 8.6 - Prob. 21ECh. 8.6 - Prob. 22ECh. 8.6 - CRUISE SHIP BOOKINGS Because of late...Ch. 8.6 - Prob. 24ECh. 8.CRQ - Fill in the blanks. A rule that assigns a number...Ch. 8.CRQ - Prob. 2CRQCh. 8.CRQ - Prob. 3CRQCh. 8.CRQ - Prob. 4CRQCh. 8.CRQ - Prob. 5CRQCh. 8.CRQ - Prob. 6CRQCh. 8.CRQ - Fill in the blanks. A probability distribution...Ch. 8.CRQ - Prob. 8CRQCh. 8.CRE - Prob. 1CRECh. 8.CRE - LIFE INSURANCE POLICIES A man purchased a 25,000,...Ch. 8.CRE - Prob. 3CRECh. 8.CRE - Prob. 4CRECh. 8.CRE - In Exercises 5-8, let Z be the standard normal...Ch. 8.CRE - Prob. 6CRECh. 8.CRE - Prob. 7CRECh. 8.CRE - Prob. 8CRECh. 8.CRE - In Exercises 9-12, let Z be the standard normal...Ch. 8.CRE - Prob. 10CRECh. 8.CRE - Prob. 11CRECh. 8.CRE - Prob. 12CRECh. 8.CRE - Prob. 13CRECh. 8.CRE - Prob. 14CRECh. 8.CRE - Prob. 15CRECh. 8.CRE - Prob. 16CRECh. 8.CRE - DRIVING AGE REQUIREMENTS The minimum age...Ch. 8.CRE - Prob. 18CRECh. 8.CRE - TRAFFIC A traffic survey of the speed of the...Ch. 8.CRE - EXPECTED PROFIT A buyer for Discount Fashions, an...Ch. 8.CRE - BOWLING A STRIKE If the probability that a bowler...Ch. 8.CRE - HEIGHTS OF WOMEN The heights of 4000 women who...Ch. 8.CRE - Prob. 23CRECh. 8.CRE - NETFLIX REVENUE FROM STREAMING SUBSCRIBERS The...Ch. 8.CRE - Prob. 25CRECh. 8.CRE - Prob. 26CRECh. 8.CRE - Prob. 27CRECh. 8.CRE - Prob. 28CRECh. 8.CRE - Prob. 29CRECh. 8.CRE - ON-TIME ARRIVALS Diane, who commutes regularly...Ch. 8.CRE - Prob. 31CRECh. 8.CRE - Prob. 32CRECh. 8.BMO - Prob. 1BMOCh. 8.BMO - Prob. 2BMOCh. 8.BMO - Prob. 3BMOCh. 8.BMO - Prob. 4BMOCh. 8.BMO - Prob. 5BMOCh. 8.BMO - A fair coin is tossed 30 times. Using the...
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