The time in years after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about five years. Suppose we randomly pick one retired individual. Find the probability that the person retired after age 70.

The probability that the person retired after age 70 is 0.1353.

Step-by-step explanation:

The random variable X is defined as the time (in years) after reaching age 60 that it takes an individual to retire.

The random variable X follows an Exponential distribution with mean, β = 5 years.

The parameter of the exponential distribution is:

The probability distribution of an Exponential distribution is:

It is provided that a person retired after age 70 years.

Then the number of years after the retirement age is, 70 - 60 = 10 years.

Compute the probability of (X > 10) as follows:

Thus, the probability that the person retired after age 70 is 0.1353.

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