1)True/False (No explanation is needed, simply write "True" or "False"):

a. When constructing a histogram, the scale for the frequency axis should begin with the minimum frequency among all the classes.

b. If events A and B are independent, then P(A and B) = P(A)P(B).

c. The Range Rule of Thumb states that approximately 68% of the data values will fall within two standard deviations of the mean.

d. One difference between bar graphs and histograms is that bar graphs are used to display categorical data, while histograms are used to display quantitative data.

e. If each of fifteen data values is equal to 20 min, then the standard deviation of the sample is equal to 20 min.

f. The sample variance is a biased estimator of the population variance because it tends to underestimate the population variance.

g. Cluster sampling is always a sound sampling method, no matter how the clusters are formed.

h. The probability of an event that is certain to occur is 1.

2)You give a housing preference survey to 500 randomly chosen undergraduate students and 500 randomly chosen graduate students, and then compare the results.

a. [2 points] What type of sampling method is used in the above example?

b. [6 points] Name two sampling methods discussed in class that are different from your answer to part (a). For each of these two methods, describe how you could conduct the housing preference survey using the given method. i. ii.

3)] A standard deck of 52 cards contains four suits (Diamonds, Hearts, Clubs, Spades), with 13 ranks per suit (A, 2, 3, ... , 10, J, Q, K). If a card is randomly selected from the deck, what is the probability it is either a 9 or a Spade?

4)Are the following pairs of events independent or dependent?

a. Event A: You roll a pair of dice. The numbers are 2 and 6.

Event B: You roll the pair of dice again. Both of the dice show the number 3.

b. Event A: You shuffle a deck of cards and randomly select one of them. It is the Queen of Hearts. You keep the card.

Event B: You randomly draw a second card from the deck. It is the 7 of Spades.

c. Event A: The instructor randomly selects a student to pass out the syllabus.

Event B: The instructor randomly selects a different student to pass out the HW.

5)Normal and Uniform Distributions:

a. [2 points] Name two characteristics of a normal distribution. i. ii.

b. [4 points] Which is more likely to have a higher variance: a data set with a normal distribution or a data set with a uniform distribution? Explain your answer.