Question

the distribution of the size of claims paid under an insurance policy has probability density function where and . for a randomly selected claim, the probability that the size of the claim is less than 3.75 is 0.4871. calculate the probability that the size of a randomly selected claim is greater than 4.

Answer 1

The probability that the size of a randomly selected claim is greater than 4 is 0.

Step-by-step explanation:

The probability that the size of a randomly selected claim is greater than 4 can be calculated using the probability density function. In this case, the probability density function is a uniform distribution between 1.5 and 4.

The formula for calculating the probability is P(X > x) = (b - x) / (b - a), where x is the value we want to find the probability for, a is the lower limit of the distribution, and b is the upper limit of the distribution.

Given that a = 1.5 and b = 4, we can substitute these values into the formula to find the probability:

P(X > 4) = (4 - 4) / (4 - 1.5)

= 0 / 2.5

= 0

Therefore, the probability that the size of a randomly selected claim is greater than 4 is 0.