The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table:discrimination over a minimum height requirement of 5 ft. 7 in. The suit claimed that this restriction eliminated more than 94% of adult females from consideration. Let x represent the height of a ran- domly selected adult woman. Suppose that x is ap- proximately normally distributed with mean 66 inches (5 ft. 6 in.) and standard deviation 2 inches.a. Is the claim that 94% of all women are shorter than 5 ft. 7 in. correct?b. What proportion of adult women would be excluded from employment as a result of the height restriction?7.118 The longest “run” of S’s in the sequence SSFSSSSFFS has length 4, corresponding to the S’s on the fourth, fifth, sixth, and seventh positions. Consider a binomial experiment with n 4, and let y be the length in the longest run of S’s.a. When p .5, the 16 possible outcomes are equally likely. Determine the probability distribution of y in this case (first list all outcomes and the y value for each one). Then calculate my.b. Repeat Part (a) for the case p .6.c. Let z denote the longest run of either S’s or F’s. Determine the probability distribution of z when p .5.7.119 Two sisters, Allison and Teri, have agreed to meet between 1 and 6 p.m. on a particular day. In fact, Allison is equally likely to arrive at exactly 1 p.m.,2 p.m., 3 p.m., 4 p.m., 5 p.m., or 6 p.m. Teri is also equally likely to arrive at each of these six times,and Allison’s and Teri’s arrival times are indepen- dent of one another. Thus there are 36 equally likely (Allison, Teri) arrival-time pairs, for example, (2, 3) or (6, 1). Suppose that the first person to arrive waits until the second person arrives; let w be the amount of time the first person has to wait.a. What is the probability distribution of w?b. On average, how much time do you expect toelapse between the two arrivals?7.120 Four people—a, b, c, and d—are waiting to give blood. Of these four, a and b have type AB blood, whereas c and d do not. An emergency call has just come in for some type AB blood. If blood dona- tions are taken one by one from the four peoplein random order and x is the number of donations needed to obtain an AB individual (so possiblex values are 1, 2, and 3), what is the probability distribution of x?7.121 Kyle and Lygia are going to play a series of Trivial Pursuit games. The first person to win four games will be declared the winner. Suppose that outcomesx 0 1 p(x) .54 .164The mean value of x is mx 1.2. Calculate the valuesofs2x andsx
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The
discrimination over a minimum height requirement of 5 ft. 7 in. The suit claimed that this restriction eliminated more than 94% of adult females from consideration. Let x represent the height of a ran- domly selected adult woman. Suppose that x is ap- proximately
a. Is the claim that 94% of all women are shorter than 5 ft. 7 in. correct?
b. What proportion of adult women would be excluded from employment as a result of the height restriction?
7.118 The longest “run” of S’s in the sequence SSFSSSSFFS has length 4, corresponding to the S’s on the fourth, fifth, sixth, and seventh positions. Consider a binomial experiment with n 4, and let y be the length in the longest run of S’s.
a. When p .5, the 16 possible outcomes are equally likely. Determine the probability distribution of y in this case (first list all outcomes and the y value for each one). Then calculate my.
b. Repeat Part (a) for the case p .6.
c. Let z denote the longest run of either S’s or F’s. Determine the probability distribution of z when p .5.
7.119 Two sisters, Allison and Teri, have agreed to meet between 1 and 6 p.m. on a particular day. In fact, Allison is equally likely to arrive at exactly 1 p.m.,
2 p.m., 3 p.m., 4 p.m., 5 p.m., or 6 p.m. Teri is also equally likely to arrive at each of these six times,
and Allison’s and Teri’s arrival times are indepen- dent of one another. Thus there are 36 equally likely (Allison, Teri) arrival-time pairs, for example, (2, 3) or (6, 1). Suppose that the first person to arrive waits until the second person arrives; let w be the amount of time the first person has to wait.
a. What is the probability distribution of w?
b. On average, how much time do you expect to
elapse between the two arrivals?
7.120 Four people—a, b, c, and d—are waiting to give blood. Of these four, a and b have type AB blood, whereas c and d do not. An emergency call has just come in for some type AB blood. If blood dona- tions are taken one by one from the four people
in random order and x is the number of donations needed to obtain an AB individual (so possible
x values are 1, 2, and 3), what is the probability distribution of x?
7.121 Kyle and Lygia are going to play a series of Trivial Pursuit games. The first person to win four games will be declared the winner. Suppose that outcomes
x 0 1 p(x) .54 .16
4
The
ofs2x andsx
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