Question

Let X have a continuous uniform distribution on the interval [5, 25]. What is the 47th percentile of this distribution?

Answer 1

The 47th percentile of a continuous uniform distribution on the interval [5, 25] is calculated using the formula for percentiles. The 47th percentile is found to be 14.4.

Step-by-step explanation:

The 47th percentile of a continuous uniform distribution on the interval [5, 25] can be found by using the formula for percentiles in a uniform distribution:

• P(th percentile) = a + (b - a) * (p / 100)

Here, 'a' is the lower bound of the distribution, 'b' is the upper bound of the distribution, and 'p' is the desired percentile.

For the given distribution:

• a = 5
• b = 25
• p = 47

Applying these values to the formula:

P(47th percentile) = 5 + (25 - 5) * (47 / 100)

P(47th percentile) = 5 + 20 * 0.47

P(47th percentile) = 5 + 9.4

P(47th percentile) = 14.4