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Chapter 5: Q 5.103 (page 223)
Fill in the blanks.
a.A relative-frequency distribution is to a variable as a ___ distribution is to a random variable.
b. A relative-frequency histogram is to a variable as a ___ histogram is to a random variable.
Part a. Probability
Part b. Probability
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In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.
Part (a) Find the mean of the random variable.
Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.
Normality Requirement What is different about the normality requirement for a confidenceinterval estimate of \(\sigma \)and the normality requirement for a confidence interval estimateof \(\mu \)?
Craps. The game of craps is played by rolling two balanced dice. A first roll of a sum of 7 or 11 wins; and a first roll of a sum of 2,3 , or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is thrown. It can be shown that the probability is 0.493 that a player wins a game of craps. Suppose we consider a win by a player to be a success,
a. Identify the success probability,
b. Construct a table showing the possible win-lose results and their probabilities for three games of craps. Round each probability to three decimal places.
c. Draw a tree diagram for part (b).
d. List the outcomes in which the player wins exactly two out of three times.
e. Determine the probability of each of the outcomes in part (d). Explain why those probabilities are equal.
f. Find the probability that the player wins exactly two out of three times.
g. Without using the binomial probability formula, obtain the probability distribution of the random variable , the number of times out of three that the player wins.
h. Identify the probability distribution in part (g).
Age and senators. According to the congressional directory, the official directory of the U.S Congress prepared by the Joint Committee on printing the age distribution for senators in the U.S Congress as of fall 2013, is as shown in the following table.
Suppose that a U.S senator is selected at random. let
A = event the senator is under 50,
B = event the senator is in his or her 50s,
C = event the senator is in his or her 60s, and
S = event the senator is under 70.
Part (a) Use the table and the f/N rule to find P(S).
Part (b) Express event S in term of event A,B and C
Part (c) Determine P(A), P(B) and P(C).
Part(d) Compute P(S), Using the special addition rule and your answers from part (b) and part(c) Compare your answer with in parts (a)
Dice. When one die is rolled, the following six outcome are possible;
List the outcome constituting
A = event the die come up even
B = event the die come up 4 or more
C event the die come up at most 2, and
D= event the die come up 3.
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