MCQs: Probability

27. In 1998, the average age of students at UTC was 22 with a standard deviation of 3.96.
In 1999, the average age was 24 with a standard deviation of 4.08. In which year do
the ages show a more dispersed distribution? Show your complete work.

29. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then
P(A  B) =
a. 0.76
b. 1
c. 0.24
d. 0.2
e. None of the above answers is correct.

30. A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9.
One chip is selected at random from each urn. The total number of sample
points in the sample space is _____
a. 30
b. 100
c. 729
d. 1,000
e. None of the above answers is correct.

31. A six-sided die is tossed 3 times. The probability of observing three ones in a row is

a. 1/3
b. 1/6
c. 1/27
d. 1/216
e. None of the above answers is correct.

32. If P(A) = 0.38, P(B) = 0.83, and P(A  B) = 0.57; then P(A  B) =
a. 1.21
b. 0.64
c. 0.78
d. 1.78
e. None of the above answers is correct.
Use this data to answer questions 34 and 35.
A sample of 2,500 people was asked how many cups of coffee they drink in the morning.
You are given the following sample information.
Cups of Coffee Frequency
0 700
1 900
2 600
3 300
2,500

34. The expected number of cups of coffee is
a. 1
b. 1.2
c. 1.5
d. 1.7
e. None of the above answers is correct.

35. The variance of the number of cups of coffee is
a. 0.96
b. 0.9798
c. 1
d. 2.4
e. None of the above answers is correct.

Please use the information in this paragraph to answer questions 36 - 40.
The random variable x is the number of occurrences of an event over an interval of ten
minutes. It can be assumed that the probability of an occurrence is the same in any two
time periods of an equal length. It is known that the that the probability of an occurrence
is the same in any two time periods of an equal length. It is known that the mean number
of occurences in ten minutes is 5.3.

36. The random variable x satisfies which of the following probability distributions?
a. normal
b. Poisson
c. binomial
d. Not enough information is given to answer this question.
e. None of the above answers is correct.

37. The appropriate probability distribution for the random variable is
a. discrete
b. continuous
c. either a or b depending on how the interval is defined
d. not enough information is given
e. None of the above answers is correct.

38. The expected value of the random variable x is
a. 2
b. 5.3
c. 10
d. 2.3
e. None of the above answers is correct.

39. The probability that there are 8 occurrences in ten minutes is
a. 0.0241
b. 0.0771
c. 0.1126
d. 0.9107
e. None of the above answers is correct.

40. The probability that there are less than 3 occurrences is
a. 0.0659
b. 0.0948
c. 0.1016
d. 0.1239
e. None of the above answers is correct.