Statistics Quiz

1. A radio station that plays classical music has a “By Request” program each Saturday night. The percentage of requests for composers on a particular night are listed below:

Composers
Percentage of Requests

Bach

5

Beethoven

26

Brahms

9

Dvorak

2

Mendelssohn

3

Mozart

21

Schubert

12

Schumann

7

Tchaikovsky

14

Wagner

1

a. Does the data listed above comprise a valid probability distribution? Explain.

b. What is the probability that a randomly selected request is for one of the three B’s?

c. What is the probability that a randomly selected request is for a Mozart piece?

d. What is the probability that a randomly selected request is not for one of the two S’s?

e. Neither Bach nor Wagner wrote any symphonies. What is the probability that a randomly selected request is for a composer who wrote at least one symphony?

f. What is the probability that a randomly selected request is for a composer other than one of the three B’s or one of the two S’s?

2. In each of the following situations, state whether or not the given assignment of probabilities to given outcomes is legitimate, that is, satisfies the rules of a probability distribution. (The assignment of probabilities need not follow common sense understanding of the outcomes!)

a. Roll a die and record the count of spots on the up face: P(1) = 0, P(2) = 1/6, P(3) = 1/3,
P(4) = 1/3, P(5) = 1/6, P(6) = 0.

b. Choose a college student at random and record sex and enrollment status:
P(female-fulltime) = 0.56,

P(female-part time) = 0.24,
P(male-fulltime) = 0.44,
P(male- part time) = 0.17

c. Deal a card from a shuffled deck: P(Clubs) = 12/52, P(Diamonds) = 12/52, P(Hearts) = 12/52,

P(Spades) = 16/52.

3. The table below describes (approximately) the distribution of a group of 2000 randomly selected adults who were asked if they were in favor of or against cloning.

In Favor
Against
No Opinion

Male

395
405
100

Female
300
680
120_______

If we were to randomly select one person from this group:

a. Find the probability that the selected person is a male.

b. Find the probability that the selected person is in favor of cloning.

c. Given that the selected person is female, what is the probability that she is in favor of cloning?

d. Given that the selected person has no opinion, what is the probability that the person is male?

e. Find the probability that the selected person is male and is against cloning.

f. Are the events the selected person is female and the selected person has no opinion independent events? Explain.

4. Data from a National Health Survey show that men’s average weight is normally distributed with a mean of 170 pounds and a standard deviation of 30 pounds.

a. If a man is chosen at random, what is the probability that his weight is greater than 180 pounds?

b. If 100 men are randomly selected, what is the probability that their mean weight is greater than 180 pounds?

c. What is the probability that mean weight of the 100 men is less than 160

pounds?

5. According to the College Board’s report, the average tuition and fees at four year private colleges and universities in the United States was $20,273 for the academic year 2002 – 2003 and the standard deviation was $4100. For a random sample of 100 four year private U.S. colleges:

a. What is the mean of the sampling distribution?

b. What is the standard deviation of the sampling distribution?

c. What is the probability that the mean tuition and fees of the sample is greater than
$20,000?

d. What is the probability that the mean tuition and fees of the sample is less than
$18,000?

e. What is the probability that the mean tuition and fees of the sample is within $410 of
the population mean?