A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. After years of commuting she has developed the following probability distribution for the number of red lights she stops at each day on her way to work:

0 1 2 3 4 5

.05 .25 .35 .15 .15 .05

Note that the standard deviation of the above probability distribution is = 1.26

How many red lights should she expect to stop at each day on her way to work?

a.3
b. 2.5
c. 2
d. 2.25
e. 0.35

Suppose each red light delays the commuter 1.5 minutes. What is the standard deviation of the number of minutes that she is delayed by red lights?

a. 2.38

b. 1.89

c. 1.59

d. 3.57

e. 2.25

Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.