time required to complete a statistics exam is uniformly distributed between 60 and 150 minutes. What is the probability that a student will take longer than 120 minutes to complete the exam
(150-120)/(150-60) = ?
To find the probability that a student will take longer than 120 minutes to complete the exam, we need to calculate the area under the probability density function (PDF) curve of the Uniform distribution beyond the value of 120.
The Uniform distribution is defined by its minimum value (a = 60) and its maximum value (b = 150). The PDF of a Uniform distribution is a constant value within this range.
To calculate the probability, we can use the formula for a Uniform distribution:
P(X > x) = (b - x) / (b - a)
where P(X > x) represents the probability of the random variable X being greater than x.
In this case, x = 120, a = 60, and b = 150. Substituting the values into the formula, we have:
P(X > 120) = (150 - 120) / (150 - 60) = 30 / 90 = 1/3
Therefore, the probability that a student will take longer than 120 minutes to complete the exam is 1/3 or approximately 0.3333.