1.If the random variable X is normally distributed with a mean of 60 and a variance of 100, then P(X >66) is:

a. 0.27

b. 0.49

c. 0.69

d. 0.89

e. None of the above

2.Suppose 30% of the BMWs sold in Australia were made in Germany. A sample of 20 BMWs were taken. What is the probability that 10 or fewer the selected BMWs were made outside Germany?

a. 0.05

b. 0.43

c. 0.95

d. 0.98

e. None of the above

3.The number of customers shopping at a local supermarket follows a Poisson distribution with a mean of 10 people per hour. The probability that over the next hour 6 people will shop at the local supermarket is:

a. 0.01

b. 0.03

c. 0.05

d. 0.06

e. None of the above

4.Consider two independent events A and B. The probability that event A occurs is 0.40 and the probability that event A occurs when event B occurs is 0.40, then P(B) is:

a. 1.0

b. 0.6

c. 0.4

d. 0.2

e. P(B) cannot be determined with the information given

5.If E(X2) is 14 and the standard deviation of X is 2, what is the value of the expected value of X?

a. 2.25

b. 3.00

c. 3.16

d. 5.50

e. None of the above

6.Consider two random variables X and Y with E(X)= 4, E(Y) = 2, E(XY) = 12, V(X) = 16 and V(Y) = 25, then the correlation coefficient between X and Y is:

a. -0.2

b. -0.3

c. 0.2

d. 0.3

e. None of the above

7.The following shows the probability distribution of the number of toys a customer buys at a store per day (X).

X 1 2 3 4 5 6 7

P(X) 0.05 0.15 0.15 0.25 0.20 0.10 0.10

The probability that more than five toys are bought is:

a. 0.10

b. 0.20

c. 0.40

d. 0.80

e. None of the above

8.What proportion of the data from a normal distribution is within 1.5 standard deviations of the mean?

a. 0.5467

b. 0.7525

c. 0.8664

d. 0.9656

e. None of the above

9.The number of customers paying with Apple Pay is Poisson distributed. The mean number of such users per 5-minute interval is 1.5. The probability that no such users in the next 10 minutes is:

a. 0.05

b. 0.22

c. 0.34

d. 0.45

e. None of the above