A student was doing a project work, involving a school survey, to find the number of hours spent on study by students on a randomly selected school day. At the end of the survey he prepared the following report related to the data.
Let x denote the number of hours spent on study by students on a randomly selected school day
then,
\(P(X = x) = \begin{cases} 0.2, & \text{if } x = 0\\ kx, & \text{if } x = 1 \text{ or } x = 2\\ k(6 - x), & \text{if } x = 3 \text{ or } x = 4\\ 0, & \text{otherwise} \end{cases}\)
where k is unknown constant
Based on the above information answer the Questions
The probability that the study time of students is at least 3 hours
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.5
The probabilities add up to 1:
\(0.2 + k + 2k + 3k + 2k = 1\)
\(k = 0.1\)
“At least 3 hours” means X = 3 or X = 4:
\(P(X \ge 3) = k(6 - 3) + k(6 - 4)\)
\(= 3k + 2k = 5k = 0.5\)