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) 0.16 0.36 0.38 0.10 1.00

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

a. P(X=50)P(X=50).
b. P(X≤75)P(X≤75).
c. P(X>50)P(X>50).
d. P(X<100)P(X<100).

Answer 1

a. P(X=50)= 0.36

b. P(X≤75) = 0.9

c. P(X>50)= 0.48

d. P(X<100) = 0.9

Explanation:

The given data is

x 25 50 75 100 Total

P(x) 0.16 0.36 0.38 0.10 1.00

Where X is the variable and P(X) = probabililty of that variable.

From the above

a. P(X=50)= 0.36

We add the probabilities of the variable below and equal to 75

b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9

We find the probability of the variable greater than 50 and add it.

c. P(X>50)= 0.38+0.10= 0.48

It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.

d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9