Question

Determine the probability that the student studied for at least 2 hours.

Hint:

For cumulative probability calculations, sum up the probabilities of all values greater than or equal to the given threshold.

Answer 1

Step 1: Calculate the probability of studying for at least 2 hours: \[P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4).\] Step 2: Insert values from the probability distribution: \[P(X \geq 2) = k(2) + k(5 - 3) + k(5 - 4).\] Step 3: Substitute \( k = 0.15 \): \[P(X \geq 2) = 0.15(2) + 0.15(2) + 0.15(1).\] Step 4: Perform the calculation: \[P(X \geq 2) = 0.3 + 0.3 + 0.15 = 0.75.\] The probability of the student studying for at least 2 hours is 0.75.