Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Question
Chapter 4.6, Problem 96E
a.
To determine
Find the value of k.
b.
To determine
Find the degrees of freedom.
c.
To determine
Find the
c.
To determine
Find the probability that Y lies within 2 standard deviations of its mean.
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Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds.
Click on the datafile logo to reference the data.
DATA file
Type of Fund
Domestic Equity
Number of Funds
Total Return (%)
9191
4.65
International Equity
2621
18.15
Hybrid
1419
2900
11.36
6.75
Specialty Stock
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)
%
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…
The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided.
Days to
Maturity
20
Dollar Value
($ millions)
20
12
30
7
10
5
6
15
10
Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds (to 1 decimal).
days
c. What are the first and third quartiles?
First Quartiles (to 1 decimals)
Third Quartiles (to 4 decimals)
× ☑
Which companies spend the most money on advertising? Business Insider maintains a list of the top-spending companies. In 2014, Procter & Gamble spent more than any other company, a whopping $5 billion. In second place was Comcast, which spent $3.08 billion (Business Insider website, December 2014). The top 12 companies and
the amount each spent on advertising in billions of dollars are as follows.
Click on the datafile logo to reference the data.
DATA file
Company
Procter & Gamble
Comcast
Advertising
($billions)
$5.00
3.08
2.91
Company
American Express
General Motors
Advertising
($billions)
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ETET
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2.44
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Toyota
Fiat Chrysler
Walt Disney Company
J.P Morgan
a. What is the mean amount spent on advertising? (to 2 decimals)
2.55
b. What is the median amount spent on advertising? (to 3 decimals)
2.09
1.97
1.96
1.88
Chapter 4 Solutions
Mathematical Statistics with Applications
Ch. 4.2 - Prob. 1ECh. 4.2 - A box contains five keys, only one of which will...Ch. 4.2 - A Bernoulli random variable is one that assumes...Ch. 4.2 - Let Y be a binomial random variable with n = 1 and...Ch. 4.2 - Suppose that Y is a random variable that takes on...Ch. 4.2 - Consider a random variable with a geometric...Ch. 4.2 - Let Y be a binomial random variable with n=10 and...Ch. 4.2 - Prob. 8ECh. 4.2 - A random variable Y has the following distribution...Ch. 4.2 - Refer to the density function given in Exercise...
Ch. 4.2 - Suppose that Y possesses the density function...Ch. 4.2 - Prob. 12ECh. 4.2 - A supplier of kerosene has a 150-gallon tank that...Ch. 4.2 - A gas station operates two pumps, each of which...Ch. 4.2 - As a measure of intelligence, mice are timed when...Ch. 4.2 - Let Y possess a density function...Ch. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - If, as in Exercise 4.17, Y has density function...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - If Y is a continuous random variable with density...Ch. 4.3 - Prob. 25ECh. 4.3 - If Y is a continuous random variable with mean ...Ch. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - The proportion of time Y that an industrial robot...Ch. 4.3 - Prob. 31ECh. 4.3 - Weekly CPU time used by an accounting firm has...Ch. 4.3 - The pH of water samples from a specific lake is a...Ch. 4.3 - Prob. 34ECh. 4.3 - If Y is a continuous random variable such that...Ch. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.4 - Suppose that Y has a uniform distribution over the...Ch. 4.4 - If a parachutist lands at a random point on a line...Ch. 4.4 - Suppose that three parachutists operate...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - A circle of radius r has area A = r2. If a random...Ch. 4.4 - Prob. 44ECh. 4.4 - Upon studying low bids for shipping contracts, a...Ch. 4.4 - 4.45 Upon studying low bids for shipping...Ch. 4.4 - The failure of a circuit board interrupts work...Ch. 4.4 - If a point is randomly located in an interval (a,...Ch. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - The cycle time for trucks hauling concrete to a...Ch. 4.4 - Refer to Exercise 4.51. Find the mean and variance...Ch. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Refer to Exercise 4.54. Suppose that measurement...Ch. 4.4 - Refer to Example 4.7. Find the conditional...Ch. 4.4 - Prob. 57ECh. 4.5 - Use Table 4, Appendix 3, to find the following...Ch. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - What is the median of a normally distributed...Ch. 4.5 - If Z is a standard normal random variable, what is...Ch. 4.5 - A company that manufactures and bottles apple...Ch. 4.5 - The weekly amount of money spent on maintenance...Ch. 4.5 - In Exercise 4.64, how much should be budgeted for...Ch. 4.5 - A machining operation produces bearings with...Ch. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Refer to Exercise 4.68. If students possessing a...Ch. 4.5 - Refer to Exercise 4.68. Suppose that three...Ch. 4.5 - Wires manufactured for use in a computer system...Ch. 4.5 - Prob. 72ECh. 4.5 - The width of bolts of fabric is normally...Ch. 4.5 - A soft-drink machine can be regulated so that it...Ch. 4.5 - The machine described in Exercise 4.75 has...Ch. 4.5 - The SAT and ACT college entrance exams are taken...Ch. 4.5 - Show that the maximum value of the normal density...Ch. 4.5 - Show that the normal density with parameters and ...Ch. 4.5 - Assume that Y is normally distributed with mean ...Ch. 4.6 - a If 0, () is defined by ()=0y1eydy, show that...Ch. 4.6 - Use the results obtained in Exercise 4.81 to prove...Ch. 4.6 - The magnitude of earthquakes recorded in a region...Ch. 4.6 - If Y has an exponential distribution and P(Y 2) =...Ch. 4.6 - Refer to Exercise 4.88. Of the next ten...Ch. 4.6 - The operator of a pumping station has observed...Ch. 4.6 - The length of time Y necessary to complete a key...Ch. 4.6 - Historical evidence indicates that times between...Ch. 4.6 - One-hour carbon monoxide concentrations in air...Ch. 4.6 - Prob. 95ECh. 4.6 - Prob. 96ECh. 4.6 - Prob. 97ECh. 4.6 - Consider the plant of Exercise 4.97. How much of...Ch. 4.6 - If 0 and is a positive integer, the...Ch. 4.6 - Prob. 100ECh. 4.6 - Applet Exercise Refer to Exercise 4.88. Suppose...Ch. 4.6 - Prob. 102ECh. 4.6 - Explosive devices used in mining operations...Ch. 4.6 - The lifetime (in hours) Y of an electronic...Ch. 4.6 - Four-week summer rainfall totals in a section of...Ch. 4.6 - The response times on an online computer terminal...Ch. 4.6 - Refer to Exercise 4.106. a. Use Tchebysheffs...Ch. 4.6 - The weekly amount of downtime Y (in hours) for an...Ch. 4.6 - If Y has a probability density function given by...Ch. 4.6 - Suppose that Y has a gamma distribution with...Ch. 4.6 - Prob. 112ECh. 4.7 - Prob. 120ECh. 4.7 - Prob. 122ECh. 4.7 - The relative humidity Y, when measured at a...Ch. 4.7 - The percentage of impurities per batch in a...Ch. 4.7 - Prob. 125ECh. 4.7 - Suppose that a random variable Y has a probability...Ch. 4.7 - Verify that if Y has a beta distribution with = ...Ch. 4.7 - Prob. 128ECh. 4.7 - During an eight-hour shift, the proportion of time...Ch. 4.7 - Prob. 130ECh. 4.7 - Errors in measuring the time of arrival of a wave...Ch. 4.7 - Prob. 132ECh. 4.7 - Prob. 133ECh. 4.7 - Prob. 134ECh. 4.7 - Prob. 135ECh. 4.9 - Suppose that the waiting time for the first...Ch. 4.9 - Prob. 137ECh. 4.9 - Example 4.16 derives the moment-generating...Ch. 4.9 - The moment-generating function of a normally...Ch. 4.9 - Identify the distributions of the random variables...Ch. 4.9 - If 1 2, derive the moment-generating function of...Ch. 4.9 - Refer to Exercises 4.141 and 4.137. Suppose that Y...Ch. 4.9 - The moment-generating function for the gamma...Ch. 4.9 - Consider a random variable Y with density function...Ch. 4.9 - A random variable Y has the density function...Ch. 4.10 - A manufacturer of tires wants to advertise a...Ch. 4.10 - A machine used to fill cereal boxes dispenses, on...Ch. 4.10 - Find P(|Y | 2) for Exercise 4.16. Compare with...Ch. 4.10 - Find P(|Y | 2) for the uniform random variable....Ch. 4.10 - Prob. 150ECh. 4.10 - Prob. 151ECh. 4.10 - Refer to Exercise 4.109. Find an interval that...Ch. 4.10 - Refer to Exercise 4.129. Find an interval for...Ch. 4.11 - A builder of houses needs to order some supplies...Ch. 4.11 - Prob. 157ECh. 4.11 - Consider the nail-firing device of Example 4.15....Ch. 4.11 - Prob. 159ECh. 4 - Prob. 160SECh. 4 - Prob. 161SECh. 4 - Prob. 162SECh. 4 - Prob. 163SECh. 4 - The length of life of oil-drilling bits depends...Ch. 4 - Prob. 165SECh. 4 - Prob. 166SECh. 4 - Prob. 167SECh. 4 - Prob. 168SECh. 4 - An argument similar to that of Exercise 4.168 can...Ch. 4 - Prob. 170SECh. 4 - Suppose that customers arrive at a checkout...Ch. 4 - Prob. 172SECh. 4 - Prob. 173SECh. 4 - Prob. 174SECh. 4 - Prob. 175SECh. 4 - If Y has an exponential distribution with mean ,...Ch. 4 - Prob. 180SECh. 4 - Prob. 181SECh. 4 - Prob. 182SECh. 4 - Prob. 183SECh. 4 - Prob. 184SECh. 4 - Prob. 185SECh. 4 - Prob. 186SECh. 4 - Refer to Exercise 4.186. Resistors used in the...Ch. 4 - Prob. 188SECh. 4 - Prob. 189SECh. 4 - Prob. 190SECh. 4 - Prob. 191SECh. 4 - The velocities of gas particles can be modeled by...Ch. 4 - Because P(YyYc)=F(y)F(c)1F(c) has the properties...Ch. 4 - Prob. 194SECh. 4 - Prob. 195SECh. 4 - Prob. 196SECh. 4 - Prob. 197SECh. 4 - Prob. 198SECh. 4 - Prob. 199SECh. 4 - Prob. 200SE
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