Homework SourseThe Student Learning Center of Franklin University surveyed
The Student Learning Center of Franklin University surveyed students to see how many tutoring hours per week each used in a trimester. The following table shows the number of hours, X, students used SLC services and their probabilities.
X = # of hours
P(x)
3
0.10
4
0.23
5
0.30
6
0.27
7+
0.10
What is the probability that a student used more than 4 hours?
What is the probability that a student used at least 6 hours?_________________________________________________________________
What is the probability that a student used at most 4 hours?_________________________________________________________________
What is the expected value of X? ___________________________________________________________________
Give at least two reasons to explain why this is a valid probability distribution:_____________________________________________________________________________ _____________________________________________________________________________
| X = # of hours | P(x) |
| 3 | 0.10 |
| 4 | 0.23 |
| 5 | 0.30 |
| 6 | 0.27 |
| 7+ | 0.10 |
Solution
probability that a student used more than 4 hours = P(5 hours) + P(6 hours) + P(7+ hours)
= 0.3 + 0.27 + 0.10
= 0.67
probability that a student used at least 6 hours = P(6 hours) + P(7+ hours)
= 0.27 + 0.10
= 0.37
probability that a student used at most 4 hours = P(3 hours) + P(4 hours)
= 0.1 + 0.23
= 0.33
expected value of X = Sum of x.p(x)
= 3 * 0.1 + 4 * 0.23 + 5 * 0.3 + 6 * 0.27 + 7 * 0.10 = 5.04
two reasons to explain why this is a valid probability distribution
Each probability is between 0 and 1 and
The sum of all of the probabilities is 1.00
