In a carnival game, a person wagers 2 on the roll of two dice. If the total of the two dice is 2, 3, 4, 5, or 6 then the person gets 4 (the 2 wager and 2 winnings).
If the total of the two dice is 8, 9, 10, 11, or 12 then the person gets nothing (loses 2). If the total of the two dice is 7, the person gets 0.75 back (loses 0.25). What is the expected value of playing the game once? A) -0.04 B) -0.42 C) 2.00 D) 0.00
Q. 2A student scores 56 on a geography test and 285 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 10.
If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class? A) The student scored better on the geography test.
B) The student scored better on the mathematics test.
C) The student scored the same on both tests.
Q. 3The peak shopping time at a pet store is between 8-11:00 am on Saturday mornings. Management at the pet store randomly selected 65 customers last Saturday morning and decided to observe their shopping habits.
They recorded the number of items that a sample of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the pet store. A) number of items - discrete; total time - continuous
B) number of items - continuous; total time - continuous
C) number of items - continuous; total time - discrete
D) number of items - discrete; total time - discrete
Q. 4Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 30 to 70. What is the probability that this experiment results in an outcome less than 40?
A) 0.25 B) 0.1 C) 0.31 D) 1
Q. 5True or False: The expected value of a discrete probability distribution may be negative.
A) True B) False
Q. 6If nothing is known about the shape of a distribution, what percentage of the observations fall within 2 standard deviations of the mean?
A) at least 75 B) at most 25
C) approximately 95 D) approximately 5
Q. 7A machine is set to pump cleanser into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that
the machine actually pumps cleanser at a rate described by the uniform distribution over the
interval 4.5 to 7.5 gallons per minute. Find the probability that between 5.0 gallons and 6.0 gallons are pumped
during a randomly selected minute.
A) 0.33 B) 0.67 C) 0 D) 1
Q. 8The number of violent crimes committed in a day possesses a distribution with a mean of 1.8 crimes per day and a standard deviation of four crimes per day.
A random sample of 80 days was observed, and the sample mean number of crimes for the sample was calculated. The data that was collected in this experiment could be measured with a __________ random variable. A) discrete B) continuous
Q. 9Suppose x is a uniform random variable with c = 30 and d = 80. Find the probability that a randomly selected observation is between 33 and 75.
A) 0.84 B) 0.16 C) 0.5 D) 0.8
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