On hot sunny summer days Jane rents inner tubes by the river

On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.

x 25 50 75 100 Total
P(x) .20 .40 .30 .10 1.00

(a) Find the probability expressions. (Round your answers to 2 decimal places.)

a. P(X = 75)

b. P(X 75)

c. P(X > 50)

d. P(X < 100)

Which of the probability expressions in parts (a)–(d) is a value of the CDF?

Part (a)

Part (b)

Part (c)

Part (d)

Solution

(a) Find the probability expressions. (Round your answers to 2 decimal places.)

a. P(X=75) = 0.30

b. P(X<=75) = P(X=25) +P(X=50) +P(X=75) = 0.20+0.40+0.30 = 0.90

c. P(X>50) = P(X=75)+P(X=100) = 0.30+0.10 = 0.40

d. P(X<100) = P(X=25)+P(X=50)+P(X=75) = 0.20+0.40+0.30 = 0.90

Which of the probability expressions in parts (a)–(d) is a value of the CDF?

Part (b) is the correct answer since it is the only option which calculates the probability of getting X=fixed value including that value.