Question

1. In a survey, Canadians were asked whether or not they thought that certain offences were serious crimes. The findings of this survey are summarized in the table, where each row lists an offence and then gives the percentage of Canadians who think that the offence is a serious crime. Assume that the findings are accurate for the population of Canadians.

Answer the questions and round your answers to 4 decimal places.

Taking towels from hotels	28%
Copying software	25%
Pirating music	17%

a) What is the probability that in a random sample of seven Canadians, exactly three think that copying software is a serious crime?

In a random sample of 80 Canadians, find the following:

b) Find the probability that exactly fourteen think that pirating music is a serious crime.

c) Find the probability that between 10 and 20 (inclusive) think that taking towels from hotels is a serious crime.

NOTE: Between a and b inclusive means a ≤ x ≤ b, it does not mean a < x < b

2. You are playing a wizard game where you roll a dice three times to collect magical artefacts. Each time you roll the dice, you collect an artefact according to these rules:

If you get a 2 or a 4, you collect a book of spells. If you get an odd number, you collect an enchanted coin. If get roll a 6, you collect a wand.

Let X be the number of books you collect. Find the probability distribution for X and give the following probabilities to 3 decimal places:

a) P(0): ?

b) P(1): ?

c) P(2): ?

d) P(3): ?

3. At a large second-hand electronics market, there are about 500 phone chargers for sale. It is found that the probability that a phone charger does not work is 18%.

You randomly choose fifteen phone chargers to buy for your student dorm without testing them. Answer the questions and round your answers to three decimal places where necessary.

a) Find the probability that none of the fifteen phone chargers "do not" work.

b) Find the probability that at least three phone chargers "do not" work.

c) Find the probability that between 5 and 7 phone chargers (inclusive) do not work.

d) Find the mean number of phone chargers that do not work.

NOTE: Between a and b inclusive means a ≤ x ≤ b, it does not mean a < x < b

Answer 1

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