A student studies for X number of hours during a randomly selected school day. The probability that X can take the values, has the following form, where k is some constant. P(X=x)= cases 0 2, & if x=0 k x, & if x=1 or 2 k(6-x), & if x=3 or 4 0, & otherwise cases The probability that the student studies for at most two hours is

Step-by-step solution

Probability of studying at most two hours The distribution must satisfy P(X = x) = 1 , where P(X=0) = 0.2 , P(X=1) = k , P(X=2) = 2k , P(X=3) = k(6-3) = 3k , and P(X=4) = k(6-4) = 2k . Summing yields 0.2 + k + 2k + 3k + 2k = 0.2 + 8k = 1 , so 8k = 0.8 and k = 0.1 . The probability P(X 2) = P(X=0) + P(X=1) + P(X=2) = 0.2 + 0.1 + 0.2 = 0.5 . 0.5