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Assignment #20

Statistics

Tanaka

Probability Distribution

1. Let x denote the number of errors contained on a randomly selected page of a book. The following table lists the probability distribution of x

x 0 1 2 3 4

P(x) .73 .16 .06 .04 .01

Find the mean and the standard deviation of x.

2. A farmer will earn a profit of $30 thousand next year in case of heavy rain, $60 thousand in case of moderate rain, and $15 thousand in case of little rain. A meteorologist forecasts that the probability is .35 for heavy rain, .40 for moderate rain, and .25 for little rain next year. Let. x be the random variable that represents next year's profits in thousands of dollars for this farmer. Write the probability distribution of x. Find the mean and standard deviation of x. Give a brief interpretation of the values of the-mean and standard deviation.

Assignment #22

Statistics

Tanaka

Binomial Distribution

1. Which of the following are binomial experiments? Explain why.

a. Rolling a die many times and observing the number of spots

b. Rolling a die many times and observing whether the number obtained is even or odd

c. Selecting a few voters from a large population of voters and observing whether or not each of them favors a certain proposition in an election when 54% of all voters are known to be in favor of this proposition

2. Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities.

a. P(x = 5) for n = 8 and p = .60

b. P(x = 3) for n = 4 and p = .30

c. P(x = 2) for n = 6 and p = .20

3. Let x be a discrete random variable that possesses a binomial distribution.

a. Using the binomial formula, write the probability distribution of x for n = 7 and p = .30 and graph it.

b. What are the mean and standard deviation of the probability distribution developed in part a.

4. A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 70% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. Assume that 70% of all people like this hamburger. On a certain day, eight customers bought it.

a. Let x denote the number of customers in this sample of eight who will like this hamburger. Using a binomial probability table, obtain the probability distribution of x and draw a graph of the probability distribution. Determine the mean and standard deviation of x.

b. Using the probability distribution of part a, find the probability that exactly three of the eight customers will like this hamburger.

Test #3 - Probability

Statistics

Tanaka

1. A group of 150 randomly selected CEOs was tested for personality type. The following table gives the results of this survey.

Type A (A)

Men (M) 78

Women (W) 19

Type B (B)

Men (M) 42

Women (W) 11

a. If one CEO is selected at random from this group, find the probability that this CEO

(i) has a type A personality.

(ii) is a woman.

(iii) is a man given that he has a type A personality.

(iv) has a type B personality given that she is a woman.

(v) has a type A personality and is a woman.

(vi

) is a man or has a type B personality

b. Are the events "woman" and "type A personality" mutually exclusive? What about the events "type A personality" and "type B personality"? Why or Why not?

c. Are the events "type A personality" and "man" independent? Why or why not?

2. A survey conducted about job satisfaction showed that 20% of workers are not happy with their current jobs. Assume that this result is true for the population of all workers. Two workers are selected at random, and it is observed whether or not they are happy with their current jobs. Draw a complete tree diagram for this problem. Find the probability that in this sample of two workers

a. both are not happy with their current jobs.

b. at least one of them is happy with their current job.

3. A random sample of 80 lawyers was taken, and they were asked if they are in favor of or against capital punishment. The following table gives the two-way classification of these 80 lawyers.

Favors (A)

Male(M) 32

Female (F) 13

Opposes (B)

Male(M)

26

Female (F)

9

a. If one lawyer is randomly selected from this group, find the probability that this lawyer

(i) favors capital punishment.

(ii) is a female.

(iii) opposes capital punishment given that the lawyer is a female.

(iv) is a male given that he favors capital punishment.

(v) is a female and favors capital punishment.

(vi) opposes capital punishment or is a male.

b. Are the events "female" and "opposes capital punishment" independent? Are they mutually exclusive? Explain why or why not?

4. In a statistics class of 45 students, 12 have a strong interest in statistics. If two students are selected at random from this class, what is the probability that both of them have a strong interest in statistics? Draw a complete tree diagram for this problem.

Subject | Mathematics |

Due By (Pacific Time) | 03/31/2014 |

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