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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