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. The standing eye height of people is normally distributed with a mean of 1567 mm with a standard deviation of 65 mm.

a) If an art work is positioned so that it is comfortable to be viewed by people with standing eye heights greater than 1450 mm, what percentage of people will find that height comfortable? Give your answer as a percentage rounded to 2 decimal places. (For example: If your answer is 67.2576 it would be rounded to 67.26. This is just an example and not the correct answer). Do not include a percent sign. Do not include a percent sign.

b) Find the 75th percentile for the standing eye level height of people. Round your answer to 2 decimal places.

3. The cholesterol content of large chicken eggs is normally distributed with a mean of 170 milligrams and standard deviation of 18 milligrams. In 35% of the eggs, the cholesterol content is less than what value? Round your answer to 3 decimal places.

4. 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): ?

5. 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

2) We are given that the standing eye height of people is normally distributed with mean 1567 mm and standard deviation of 65 mm.

a) We are asked to find the percentage of people who will find the new standing eye height greater than 1450 comfortable.

We are asked to find P(X>1450) which can be found by calculating the z-score.

Basically we will now find P(Z>-1.8).

We know that P(Z>-a)=P(Z<a).

Hence P(Z>-1.8)=P(Z<1.8) which is 0.9641.

Converting into percentage we have 96.41.

Hence 96.41 is the percentage of people who will find the new height comfortable.

b) We are asked to find the 75th percentile for the standing eye height of people.

Basically we are asked to find P(X<x)=0.75.

So we look into the standard normal table for the z-score corresponding to the value 0.75.

From the standard normal tables we come across two z-scores with values close to 0.75 namely, 0.67 and 0.68 with 0.7486 and 0.7517 respectively.

To get the exact z-score we interpolate as follows:

this represents the proportional distance from top.

Hence the required z-score is 0.6745.

Now we use the z-score formula to find the 75th percentile.

Therefore the 75th percentile for the standing eye height level is 1610.84 mm.

3) We are given that cholesterol content of large chicken eggs is normally distributed with mean of 170 milligrams and standard deviation of 18 milligrams and are asked to find that in 35% of the eggs the cholesterol content is less than what value.

So the question is asking us to find P(X<x)=0.35.

Looking at the standard normal table for z-score corresponding to value of 0.35, we come across two values close to 0.35 namely, 0.3520 and 0.3483 corresponding to z-scores of -0.38 and -0.39 respectively.

We perform interpolation to get the more approximate z-score corresponding to 0.35.

Hence -0.3854 is the required z-score.

Now using the z-score formula, we can find in 35% of the eggs the cholesterol content is less than the value,

Hence in 35% of the eggs, the cholesterol content is less than 163.063 milligrams.

Note:-Not sure about the other questions so I did not attempt it.