STATISTICS TEST # 2 |

**This is a 2-hour test.**

**Numbers in parentheses ( ) are mark values.**

In each question list the information given and show your work:

1/ Convert each of the following probabilities to odds:

a) The probability of a win by the Hawiian Pineapples

hockey team in their next game is 4/50.

b) If a researcher randomly selected 4 of 75 women to be included in a study,

the probability is 4/75 that any particular woman will be included. (4)

2/ Convert each of the following odds to probabilities:

a) The odds are 15 to 3 that a given horse will win the Kentucky Derby.

b) The odds are 99 to 1 that my raffle ticket will not win me a trip to the Bahamas. (4)

3/ What 2 conditions must be met for a function to serve as a

probability distribution for a random variable? (2)

4/ Which of the following can be a probability distribution? Justify your answer.

a) f(x) = x/10 for x = 0, 1, 2, 3, 4

b) f(1) = .25, f(2) = .30, f(3) = .15, f(4) = .15, for x = 1, 2, 3, or 4.

c) f(x) = (x - 3) / 7 for x = 0, 1, 2, 3, 4, 5. (6)

5/ The probabilities that a customer entering a bookstore buys 0, 1, 2, 3, 4, or 5 books

are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively.

(a) Find the mean of this probability distribution.

(b) __use the computing formula__ to find its variance and standard deviation. (5)

6/a) Using the formulae, find µ and s for a binomial distribution with n = 64 and p = 0.50. (2)

b) What does Chebyshev's theorem say about the probability of a random

variable distributed as in part a) taking on the values between 24 and 40? (3)

7/ The editor of women's magazine claims that it is read by 60% of the

women students at McGill. Assuming her claim is true, use the Binomial Table

to find the probabilities that among 10 women students randomly selected at McGill:

a) more than 2 read the magazine;

b) exactly 6 read the magazine;

c) at most 2 read the magazine; (6)

8/ The number of inquiries Harriet got in response to a newspaper ad

listing her piano for sale is a random variable having the Poisson distribution

with µ = 4.4. What are the probabilities that in response to her ad, she will receive:

a) exactly 2 inquiries
b) exactly 3 inquiries
c) at most 3 inquiries?

Note: e^{ - 4.4} = 0.012 (6)

9/ The yearly number of major earthquakes in the world is a random variable having __approximately__ the normal distribution with µ = 20.8 and s = 4.5.

Find the probabilities that in any given year, there will be:

a) exactly 18 major earthquakes;

b) at least 18 major earthquakes;

c) at most 16 major earthquakes. (6)

MAKE A DIAGRAM FOR EACH PART OF THE NEXT 2 QUESTIONS!!

10/ Find the standard-normal curve area which lies:

a) between z = -0.33 and z = 0.95;

b) to the right of z = -0.55;

c) to the left of z = 2.43; (3)

11/ Find z if the standard-normal-curve area

a) between -z and z is 0.4726;

b) to the left of z is 0.8888;

c) to the right of z is 0.7704; (3)

TOTAL (50)

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