Question

Question 1: Jane must pass through five traffic lights on her way to work and will have to stop at each one that is red. The probability that the number of red lights she hits when she goes to work is: Number of red lights 0 1 2 3 4 5 Probability 0.05 0.15 ??? 0.10 0.15 0.05 a. Find “???”. b. How many red lights should she expect to hit each day? c. What is the standard deviation?

Answer 1

(a)

For a valid probability distribution, sum of probabilities must be equal to 1 so

Hence, the missing probability is 0.50.

(b)

Following table shows the calculations:

X	P(X=x)	xP(X=x)	x^2*P(X=x)
0	0.05	0	0
1	0.15	0.15	0.15
2	0.5	1	2
3	0.1	0.3	0.9
4	0.15	0.6	2.4
5	0.05	0.25	1.25
Total	1	2.3	6.7

The expected number of red lights she hit each day is

(c)