Question

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) .24 .33 .29 .14 1.00 (a) Find the probability expressions: (Round your answers to 2 decimal places.) a. P(X = 25) b. P(X ≤ 50) c. P(X > 25) d. P(X < 75) (b) Which of the probability expressions in parts (a)–(d) is a value of the CDF? Part (a) Part (b) Part (c) Part (d)

Answer 1

Given that, the probabilitiy distribution is :

x	25	50	75	100
P(x)	0.24	0.33	0.29	0.14

Using this table find the following probabilities,

a) P(X = 25) = 0.24

b) P(X ≤ 50) = P(X = 25) + P(X = 50)

=> P(X ≤ 50) = 0.24 + 0.33

=> P(X ≤ 50) = 0.57

c) P(X > 25) = 1 - P(X = 25)

=> P(X > 25) = 1 - 0.24

=> P(X > 25) = 0.76

d) P(X < 75) = P(X = 25) + P(X = 50)

=> P(X < 75) = 0.24 + 0.33

=> P(X < 75) = 0.57

From given probabilitiy expressions part b) is a value of the CDF