Statistics: The Art and Science of Learning from Data (4th Edition)
Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 6, Problem 52CP

Grandparents Let X = the number of living grandparents that a randomly selected adult American has. According to recent General Social Surveys, its probability distribution is approximately P(0) = 0.71, P(1) = 0.15, P(2) = 0.09, P(3) = 0.03, P(4) = 0.02.

  1. a. Does this refer to a discrete or a continuous random variable? Why?
  2. b. Show that the probabilities satisfy the two conditions for a probability distribution.
  3. c. Find the mean of this probability distribution.

a.

Expert Solution
Check Mark
To determine

Identify whether the random variable X is discrete or continuous.

Answer to Problem 52CP

The random variable X is discrete.

Explanation of Solution

The given information is that the random variable X is the number of living grandparents of a randomly selected American adult. From the survey, the probability distribution is approximately P(0)=0.71,P(1)=0.15,P(2)=0.09,P(3)=0.03 and P(4)=0.02.

Discrete random variable:

If the random variables, consider a set of distinct possible values for the trial then it is called discrete random variable.

Continuous random variable:

If the random variables, consider the possible values and it form an interval then it is called continuous random variable

In the given situation, the random variable X represents the number of grandparents and it will be a distinct number because the number of grandparents does not be in an interval.

Thus, the random variable X is discrete.

b.

Expert Solution
Check Mark
To determine

Show that the probability values satisfy the probability distribution conditions.

Explanation of Solution

Conditions for the probability distribution:

  1. 1. For every value of x, the value of probability will lie between 0 and 1.
  2. 2. The total of all probabilities for the possible values of x is equal to 1.

From the given information, the all probability values lie between 0 and 1.

The sum of probabilities is,

P(0)+P(1)+P(2)+P(3)+P(4)=0.71+0.15+0.09+0.03+0.02=1

Therefore, the total sum of probability distribution is 1.

Thus, the probability values satisfy the probability distribution conditions.

c.

Expert Solution
Check Mark
To determine

Calculate the mean of the probability distribution.

Answer to Problem 52CP

The mean of the probability distribution is 0.50.

Explanation of Solution

Calculation:

The formula for mean is,

μ=xP(x)

From the probability distribution, calculate the mean value for number of grandparents is,

μ=(0×P(0))+(1×P(1))+(2×P(2))+(3×P(3))+(4×P(4))=(0×0.15)+(1×0.15)+(2×0.09)+(3×0.03)+(4×0.02)=0+0.15+0.18+0.09+0.08=0.50

Thus, the mean value is 0.50.

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Chapter 6 Solutions

Statistics: The Art and Science of Learning from Data (4th Edition)

Ch. 6.1 - Profit and the weather From past experience, a...Ch. 6.1 - Buying on eBay You are watching two items posted...Ch. 6.1 - Selling at the right price Some companies, such as...Ch. 6.1 - Uniform distribution A random number generator is...Ch. 6.1 - TV watching A social scientist uses the General...Ch. 6.2 - Probabilities in tails For a normal distribution,...Ch. 6.2 - Probability in graph For the normal distributions...Ch. 6.2 - Empirical rule Verify the empirical rule by using...Ch. 6.2 - Central probabilities For a normal distribution,...Ch. 6.2 - z-score for given probability in tails For a...Ch. 6.2 - Probability in tails for given z-score For a...Ch. 6.2 - z-score for right-tail probability a. For the...Ch. 6.2 - Prob. 23PBCh. 6.2 - Prob. 24PBCh. 6.2 - Prob. 25PBCh. 6.2 - Coffee Machine Suppose your favorite coffee...Ch. 6.2 - Energy use An energy study in Gainesville,...Ch. 6.2 - Birth weight for boys In the United States, the...Ch. 6.2 - MDI The Mental Development Index (MDI) of the...Ch. 6.2 - Quartiles and outliers Refer to the previous...Ch. 6.2 - April precipitation Over roughly the past 100...Ch. 6.2 - Tall enough to ride? A new roller coaster at an...Ch. 6.2 - SAT versus ACT SAT math scores follow a normal...Ch. 6.2 - Relative height Refer to the normal distributions...Ch. 6.3 - Kidney transplants In kidney transplantations,...Ch. 6.3 - Compatible donors Refer to the previous exercise....Ch. 6.3 - Symmetric binomial Construct a graph similar to...Ch. 6.3 - Number of girls in a family Each newborn baby has...Ch. 6.3 - Prob. 39PBCh. 6.3 - Prob. 40PBCh. 6.3 - Passing by guessing A quiz in a statistics course...Ch. 6.3 - NBA shooting In the National Basketball...Ch. 6.3 - Season performance Refer to the previous exercise....Ch. 6.3 - Is the die balanced? A balanced die with six sides...Ch. 6.3 - Prob. 45PBCh. 6.3 - Prob. 46PBCh. 6.3 - Prob. 47PBCh. 6.3 - Checking guidelines For Example 13 on the gender...Ch. 6.3 - Class sample Four of the 20 students (20%) in a...Ch. 6.3 - Prob. 50PBCh. 6.3 - Binomial assumptions For the following random...Ch. 6 - Grandparents Let X = the number of living...Ch. 6 - Straight or boxed? Consider a Pick-3 lottery such...Ch. 6 - Auctioning paintings A collector is interested in...Ch. 6 - Prob. 55CPCh. 6 - Are you risk averse? You need to choose between...Ch. 6 - Flyers insurance An insurance company sells a...Ch. 6 - Normal probabilities For a normal distribution,...Ch. 6 - Prob. 59CPCh. 6 - Prob. 60CPCh. 6 - Quartiles If z is the positive number such that...Ch. 6 - Boys and girls birth weight Exercise 6.28...Ch. 6 - Cholesterol The American Heart Association reports...Ch. 6 - Female heights Female heights in North America...Ch. 6 - Cloning butterflies The wingspans of recently...Ch. 6 - Gestation times For 5459 pregnant women using...Ch. 6 - Used car prices Data from the Web site carmax.com...Ch. 6 - Used car deals Refer to the previous exercise....Ch. 6 - Global warming Suppose that weekly use of gasoline...Ch. 6 - Fast-food profits Macs fast-food restaurant finds...Ch. 6 - Metric height A Dutch researcher reads that male...Ch. 6 - Manufacturing tennis balls According to the rules...Ch. 6 - Brides choice of surname According to a study done...Ch. 6 - Prob. 74CPCh. 6 - Prob. 75CPCh. 6 - Prob. 76CPCh. 6 - Weather A weather forecaster states, The chance of...Ch. 6 - Dating success Based on past experience, Julio...Ch. 6 - Canadian lottery In one Canadian lottery option,...Ch. 6 - Likes on Facebook A large retail chain sends out...Ch. 6 - Likes with online credit The retail chain from the...Ch. 6 - Which distribution for sales? A salesperson uses...Ch. 6 - Best of five Example 2 gave the probability...Ch. 6 - Prob. 84CPCh. 6 - Prob. 85CPCh. 6 - Longest streak made In basketball, when the...Ch. 6 - Airline overbooking For the Boston to Chicago...Ch. 6 - Prob. 89CPCh. 6 - Prob. 90CPCh. 6 - Prob. 91CPCh. 6 - Prob. 92CPCh. 6 - Prob. 93CPCh. 6 - Prob. 94CPCh. 6 - Prob. 95CPCh. 6 - Prob. 96CPCh. 6 - Prob. 97CPCh. 6 - Prob. 98CPCh. 6 - Prob. 99CPCh. 6 - Prob. 100CPCh. 6 - Prob. 101CP
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