MAT 202 Random Variables Checkpoint 1

Module Random Variables


Random Variables Checkpoint 1
Step 1 of 1

The first three questions refer to the following information:

The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability
distribution:

x 0 1 2 3 4 5
P(X=x) 0.20 0.30 0.20 0.15 0.10 0.05

Question 1 of 4 Points: 10 out of 10
What is the probability that in a given week there will be at most 3 accidents?

0.70
0.85
0.35
0.15
1.00
Good job! P(X ≤ 3) = .20 + .30 + .20 + .15 = .85 or P(X ≤ 3) = 1 - P(X ≤ 4) = 1 - (.10 + .05) = 1 - .15 = .85

Question 2 of 4 Points: 10 out of 10
By the third day of a particular week, 2 accidents have already occurred in the intersection. What is the probability that there will be
less than a total of 4 accidents during that week?

1.00

, 0.90
0.85
0.70
0.50
Good job! We are given that 2 accidents have already happened. In other words, we are given X≥2 and we need to find how likely X
is to be less than 4.




Question 3 of 4 Points: 10 out of 10
On average, how many accidents are there in the intersection in a week?

5.3
2.5
1.8
0.30
0.1667
Good job! We need to find the mean of X, µx. µx = 0 * .20 + 1 * .30 + 2 * .20 + 3 * .15 + 4 * .10 + 5 * .05 = 1.8

Question 4 of 4 Points: 10 out of 10
The following three histograms represent the probability distributions of the three random variables X, Y, and Z.