Question

A small train at an amusement park is carrying passengers. one-fourth of the passengers are 5 years old, 12 of the passengers are 6 years old, 18 are 7 years old, and 18 are 9 years old. what is the expected age for one of the passengers on the train?

Answer 1

The expected age for one of the passengers on the train is 91.25 years.

To find the expected age for one of the passengers on the train, we need to calculate the weighted average of the ages based on the given distribution of passengers.

Let A5 be the number of 5-year-olds, A6 for 6-year-olds, A7 for 7-year-olds, and A9 for 9-year-olds.

Given:

A5 = 1/4 of total passengers

A6 = 12

A7 = 18

A9 = 18

Assuming T is the total number of passengers, we have:

A5 = 1/4 * T

Now, the expected age (E) can be calculated using the formula:

E = (∑ (Ai * Agei)) / T

Substitute the known values:

E = ((1/4 * T * 5) + (12 * 6) + (18 * 7) + (18 * 9)) / T

Simplify the expression:

E = (5T + 72 + 126 + 162) / (4T)

E = (5T + 360) / (4T)

As the total number of passengers T cancels out, the expected age is independent of the total number of passengers.