Textbook

Data Management McGraw-Hill
Chapter

Chapter 4
Section

Chapter Review Probability Distribution

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Solutions
16 Videos

Classify each random variable as discrete or continuous.

a) length of time you play in a hockey game

b) number of times you successfully shoot a basket in a basketball game

c) number of candies in a bag

d) mass of candies in a bag

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Q1

Graph each distribution using a probability histogram.

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Q2a

Graph each distribution using a probability histogram.

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Q2b

Calculate the expectation

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Q3a

Calculate the expectation

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Q3b

Describe the criteria for a distribution to be uniform.

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Q4

A spinner has six' equal sectors, numbered from 1 to 6.

a) Show the probability distribution for a single spin, using a table and a graph.

b) Calculate the expected outcome. Interpret its meaning.

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Q5

An urn contains 25 balls, 40% of which are green. A contestant reaches in the urn to choose three balls; the contestant will win $200 if he or she selects a green ball, but will lose $120 for any other colour. Is each version of the game a fair game? Justify your response.

a) The ball is replaced after each draw.

b) The ball is not replaced after each draw.

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Q6

Prepare a distribution table and probability histogram for the number of 55 when a die is rolled six times.

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Q7

The chart shows the percent of Canadians with each blood type.

a) If 120 people are donating blood, what is the expected number of people with type 0 blood? Why would this be considered a binomial distribution?

b) Calculate the expected number of people with each of the other types of blood.

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Q8

A restaurant gives customers a card with each purchase; customers scratch a box to see if they have won a prize. Twelve percent of the cards are winners.

a) What is the probability of winning a prize only once in 10 tries?

b) What is the probability of winning a prize at least three times in 10 tries?

c) What is the expected number of winning cards in 10 tries?

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Q9

a) Prepare a table and a graph for a hypergeometric distribution with `n = 25, a = 10`

and `r = 7`

.

b) Calculate the expected outcome using two methods.

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Q10

In a collection of 56 coins, 18 are rare. If you select 10 of the coins, what is the probability that

a) all of them are rare?

b) none of them is rare?

c) at least two of them are rare?

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Q11

The fisheries department caught and tagged 420 seals. Recently, 100 seals were caught and 42 had been tagged. Estimate the size of the seal population.

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Q12

Classify each situation as uniform, binomial, hypergeometric, or none of these.

a) Forty-five percent of women aged 18 to 25 are currently enrolled in post- secondary education. The random variable is the number of women between the ages of 18 and 25, out of 25 polled, who attend post-secondary education.

b) Twenty out of 30 people at a party are nonâ€”smokers. The random variable is the number of smokers in a selection of 8 partiers.

c) The flaws in pieces of timber average 0.2 per metre. The random variable is the number of flaws in the next 50 m of timber.

d) A spinner has 20 equally likely spaces, numbered from 1 to 20. The random variable is the number on which the spinner lands.

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Q13

a) Seven cards are dealt from a standard deck. What is the probability that five are face cards?

b) Seven cards are chosen from a standard deck. with replacement. What is the probability that five are face cards?

c) Compare the two answers in parts a) and b). Explain any differences.

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Q14