Question
Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the value x, has the following form, where k is some unknown constant.
(a) Find the value of k.
(b). What is the probability that you study at least two hours ? Exactly two hours ? At most two hours?
Solution
The probability distribution of X is
|
X |
0 |
1 |
2 |
3 |
4 |
|
P(X) |
0.1 |
k |
2 k |
2k |
k |
(a) We know that
(b) P(you study at least two hours) = P(X ≥ 2)
= P(X = 2) + P(X = 3) + P(X = 4)
= 2k + 2k + k = 5k = 5 × 0.15 = 0.75
P(you study exactly two hours) = P(X = 2)
= 2k = 2 × 0.15 = 0.3
P(you study at most two hours) = P(X ≤ 2)
= P(X = 0) + P(X = 1) + P(X = 2)
= 0.1 + k + 2k = 0.1 + 3k
= 0.1 + 3 × 0.15 = 0.55
