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: The probability of the student studying for at least 2 hours is given by: \[ P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4). \] Step 2: Substitute the values from the given 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: Compute the value: \[ P(X \geq 2) = 0.3 + 0.3 + 0.15 = 0.75. \] Thus, the probability that the student studied for at least 2 hours is **0.75**.