What is the income distribution of super shoppers? Asupermarket super shopperis defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.

Income range

5-15

15-25

25-35

35-45

45-55

55 or more

Midpointx

10

20

30

40

50

60

Percent of super shoppers

21%

15%

20%

17%

18%

9%

(a)

Using the income midpointsxand the percent of super shoppers, do we have a valid probability distribution? Explain.

No. The events are indistinct and the probabilities sum to 1.Yes. The events are distinct and the probabilities do not sum to 1.Yes. The events are distinct and the probabilities sum to 1.Yes. The events are indistinct and the probabilities sum to less than 1.No. The events are indistinct and the probabilities sum to more than 1.

(b)

Use a histogram to graph the probability distribution of part (a). (Select the correct graph.)

(c)

Compute the expected incomeof a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)

=thousands of dollars

(d)

Compute the standard deviationfor the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)

=thousands of dollars

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A particular lake is known to be one of the best places to catch a certain type of fish. In this table,x= numberof fish caught in a6-hourperiod. The percentage data are the percentages of fishermen who caughtxfishin a6-hourperiod while fishing from shore.

x

0

1

2

3

4 or more

%

43%

35%

15%

6%

1%

(a)

Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.)

(b)

Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)

(c)

Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)

(d)

Compute, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)

=fish

(e)

Compute, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)

=fish

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Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (i.e., straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided.

x= age

60

61

62

63

64

P(death at this age)

0.01105

0.01381

0.01678

0.01996

0.02293

Jim is applying to Big Rock Insurance Company for his term insurance policy.

(a)

What is the probability that Jim will die in his 60th year? (Enter a number. Enter your answer to five decimal places.)

Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance (in dollars)? (Enter a number. Round your answer to two decimal places.)

$

(b)

What is the expected cost to Big Rock Insurance for years 61, 62, 63, and 64 (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.)

year 61 $

year 62 $

year 63 $

year 64 $

What would be the total expected cost to Big Rock Insurance over the years 60 through 64 (in dollars)? (Enter a number. Round your answer to two decimal places.)

$

(c)

If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Jim's death, how much should it charge for the policy (in dollars)? (Enter a number. Round your answer to two decimal places.)

$

(d)

If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make (in dollars)? (Enter a number. Round your answer to two decimal places.)

$

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Consider a binomial experiment withn=6trials where the probability of success on a single trial isp=0.25. (For each answer, enter a number. Round your answers to three decimal places.)

(a)

FindP(r= 0).

(b)

FindP(r1) by using the complement rule.

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Sociologists say that80%of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose thatsixmarried women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.)

(a)

All of them dislike their mother-in-law.

(b)

None of them dislike their mother-in-law.

(c)

At leastfourof them dislike their mother-in-law.

(d)

No more thanthreeof them dislike their mother-in-law.

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Suppose approximately80%of all marketing personnel are extroverts, whereas about55%of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.)

(a)

At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?

What is the probability that 5 or more are extroverts?

What is the probability that all are extroverts?

(b)

In a group of5computer programmers, what is the probability that none are introverts?

What is the probability that3or more are introverts?

What is the probability that all are introverts?

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Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about 6.9. Use the criterion that it is unusual to have data values more than 2.5 standard deviations above the mean or 2.5 standard deviations below the mean to answer the following questions.

(a)

Would it be unusual to have more than 120 successes out of 200 trials? Explain.

Yes. 120 is more than 2.5 standard deviations above the expected value.Yes. 120 is more than 2.5 standard deviations below the expected value.No. 120 is less than 2.5 standard deviations above the expected value.No. 120 is less than 2.5 standard deviations below the expected value.

(b)

Would it be unusual to have fewer than 40 successes out of 200 trials? Explain.

Yes. 40 is more than 2.5 standard deviations above the expected value.Yes. 40 is more than 2.5 standard deviations below the expected value.No. 40 is less than 2.5 standard deviations above the expected value.No. 40 is less than 2.5 standard deviations below the expected value.

(c)

Would it be unusual to have from 70 to 90 successes out of 200 trials? Explain.

Yes. 70 to 90 observations is within 2.5 standard deviations of the expected value.No. 70 to 90 observations is within 2.5 standard deviations of the expected value.Yes. 70 observations is more than 2.5 standard deviations below the expected value.No. 90 observations is more than 2.5 standard deviations above the expected value.

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The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample oftwelvesyringes taken from the batch. Suppose the batch contains5%defectivesyringes.

(a)

Make a histogram showing the probabilities ofr= 0, 1, 2, 3, ...,11and12defective syringes in a random sample oftwelvesyringes.(Select the correct graph.)

(b)

Find(in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.)

=syringes

What is the expected number of defective syringes the inspector will find? (Enter a number. Enter your answer to two decimal places.)

syringes

(c)

What is the probability that the batch will be accepted? (Enter a number. Round your answer to three decimal places.)

(d)

Find(in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)

=syringes

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Innocent until proven guilty? In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. (Source: The Book of Risks, by Larry Laudan, John Wiley and Sons) Suppose you are a news reporter followingtwelvecriminal trials. (For each answer, enter a number.)

(a)

If the trials were in Japan, what is the probability that all the defendants would be found guilty? (Round your answer to three decimal places.)

What is this probability if the trials were in the United States? (Round your answer to three decimal places.)

(b)

Of thetwelvetrials, what is the expected number of guilty verdicts in Japan? (Round your answer to two decimal places.)

verdicts

What is the expected number in the United Sates? (Round your answer to two decimal places.)

verdicts

What is the standard deviation in Japan? (Round your answer to two decimal places.)

verdicts

What is the standard deviation in the United States? (Round your answer to two decimal places.)

verdicts

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Use thegeometric probability distributionto solve the following problem.

On the leeward side of the island of Oahu, in a small village, about77%of the residents are of Hawaiian ancestry. Letn= 1, 2, 3, ... represent the number of people you must meet until you encounter thefirstperson of Hawaiian ancestry in the village.

(a)

Write out a formula for the probability distribution of the random variablen. (Enter a mathematical expression.)

P(n) =

(b)

Compute the probabilities thatn= 1,n= 2, andn= 3. (For each answer, enter a number. Round your answers to three decimal places.)

P(1) =

P(2) =

P(3) =

(c)

Compute the probability thatn4.Hint:P(n4) = 1P(n= 1)P(n= 2)P(n= 3). (Enter a number. Round your answer to three decimal places.)

(d)

What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry?Hint: Usefor the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.)

residents

Given

P(A) =0.4and

P(B) =0.8,

do the following. (For each answer, enter a number.)

(a)

IfAandBare independent events, computeP(AandB).

(b)

IfP(A|B) =0.1, computeP(AandB).

question

Sociologists say that90%of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose thatsevenmarried women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.)

(a)

All of them dislike their mother-in-law.

(b)

None of them dislike their mother-in-law.

(c)

At leastfiveof them dislike their mother-in-law.

(d)

No more thanfourof them dislike their mother-in-law.

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There aresevenwires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use.Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested. (Hint:There aresevenchoices for the first wire,sixfor the second wire,fivefor the third wire, etc. Enter an exact number.)

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ComputeP_7,2. (Enter an exact number.)

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Which of the following are continuous variables, and which are discrete?

(a)

number of traffic fatalities per year in the state of Florida

continuousdiscrete

(b)

distance a golf ball travels after being hit with a driver

continuousdiscrete

(c)

time required to drive from home to college on any given day

continuousdiscrete

(d)

number of ships in Pearl Harbor on any given day

continuousdiscrete

(e)

your weight before breakfast each morning

continuousdiscrete

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ComputeC_5,3. (Enter an exact number.)

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Consider the probability distribution shown below.

x

0

1

2

P(x)

0.75

0.20

0.05

Compute the expected value of the distribution. (Enter a number.)

Compute the standard deviation of the distribution. (Enter a number. Round your answer to four decimal places.)

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Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Similarities and Differences in a Random Sample of 375 Married Couples

Number of Similar Preferences

Number of Married Couples

All four

29

Three

127

Two

113

One

67

None

39

Suppose that a married couple is selected at random.

(a)

Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal places.)

0

1

2

3

4

(b)

Do the probabilities add up to 1? Why should they?

Yes, because they do not cover the entire sample space.No, because they do not cover the entire sample space.Yes, because they cover the entire sample space.No, because they cover the entire sample space.

What is the sample space in this problem?

0, 1, 2, 3 personality preferences in common1, 2, 3, 4 personality preferences in common0, 1, 2, 3, 4, 5 personality preferences in common0, 1, 2, 3, 4 personality preferences in common

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For each of the following situations, explain why the combinations rule or the permutations rule should be used.

(a)

Determine the number of different groups of 5 items that can be selected from 12 distinct items.

Use the combinations rule, since the number of arrangements within each group is of interest.Use the combinations rule, since only the items in the group is of concern.Use the permutations rule, since the number of arrangements within each group is of interest.Use the permutations rule, since only the items in the group is of concern.

(b)

Determine the number of different arrangements of 5 items that can be selected from 12 distinct items.

Use the combinations rule, since the number of arrangements within each group is of interest.Use the combinations rule, since only the items in the group is of concern.Use the permutations rule, since the number of arrangements within each group is of interest.Use the permutations rule, since only the items in the group is of concern.

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What is the law of large numbers?

As the sample size decreases, the relative frequency of outcomes gets closer to the theoretical probability of the outcome.As the sample size increases, the cumulative frequency of outcomes gets closer to the theoretical probability of the outcome.As the sample size increases, the relative frequency of outcomes gets closer to the theoretical probability of the outcome.As the sample size increases, the relative frequency of outcomes moves further from the theoretical probability of the outcome.

If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

It would be better to use 500 trials, because the law of large numbers would take effect.It would be better to use 100 trials, because the law of large numbers would take effect.It would be better to use 500 trials, because 100 trials is always too small.It would be better to use 100 trials, because 500 trials is always too big.

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A recent survey of1010U.S. adults selected at random showed that661consider the occupation of firefighter to have very great prestige.Estimate the probability (to the nearest hundredth) that aU.S. adultselected at random thinks the occupation of firefighter has very great prestige. (Enter a number.)

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The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample ofeightsyringes taken from the batch. Suppose the batch contains1%defectivesyringes.

(a)

Make a histogram showing the probabilities ofr= 0, 1, 2, 3, ...,7and8defective syringes in a random sample ofeightsyringes.(Select the correct graph.)

(b)

Find(in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.)

=syringes

What is the expected number of defective syringes the inspector will find? (Enter a number. Enter your answer to two decimal places.)

syringes

(c)

What is the probability that the batch will be accepted? (Enter a number. Round your answer to three decimal places.)

(d)

Find(in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)

=syringes

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What is the income distribution of super shoppers? Asupermarket super shopperis defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.

Income range

5-15

15-25

25-35

35-45

45-55

55 or more

Midpointx

10

20

30

40

50

60

Percent of super shoppers

20%

13%

22%

17%

19%

9%

(a)

Using the income midpointsxand the percent of super shoppers, do we have a valid probability distribution? Explain.

No. The events are indistinct and the probabilities sum to more than 1.Yes. The events are indistinct and the probabilities sum to less than 1.Yes. The events are distinct and the probabilities sum to 1.No. The events are indistinct and the probabilities sum to 1.Yes. The events are distinct and the probabilities do not sum to 1.

(b)

Use a histogram to graph the probability distribution of part (a). (Select the correct graph.)

(c)

Compute the expected incomeof a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)

=thousands of dollars

(d)

Compute the standard deviationfor the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)

=thousands of dollars

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A particular lake is known to be one of the best places to catch a certain type of fish. In this table,x= numberof fish caught in a6-hourperiod. The percentage data are the percentages of fishermen who caughtxfishin a6-hourperiod while fishing from shore.

x

0

1

2

3

4 or more

%

43%

35%

15%

6%

1%

(a)

Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.)

(b)

Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)

(c)

Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)

(d)

Compute, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)

=fish

(e)

Compute, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)

=fish

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What is the probability of the following. (For each answer, enter an exact number.)

(a)

An eventAthat is certain to occur?

(b)

An eventBthat is impossible?

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The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

(a)

Are the outcomes on the two cards independent? Why?

No. The events cannot occur together.Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.Yes. The events can occur together.No. The probability of drawing a specific second card depends on the identity of the first card.

(b)

FindP(ace on 1st cardandqueenon 2nd). (Enter your answer as a fraction.)

(c)

FindP(queenon 1st cardandace on 2nd). (Enter your answer as a fraction.)

(d)

Find the probability of drawing an aceandaqueenin either order. (Enter your answer as a fraction.)