the average age of private vehicles in Marilao Bulacan is 6 years. Assume that the standard deviation is 2 years. A random sample of 10 private vehicles is chosen, find the probability that the mean of private vehicles ages is

a. between 3 to 9 years

b. over 6 years

This answer was edited.Here, we assume that the average age of private vehicles in Marilao Bulacan is normally distributed.

Let be a random variable representing the average age of private vehicles in Marilao Bulacan from a sample of size , then the probability that is less than a value is given by , where is the population mean and is the population standard deviation.

Here, , , and .

a.) Thus, the probability that the mean of private vehicles ages is between 3 to 9 years is given by

Using the table of areas under the standard normal curve or a calculator, we have .

Therefore, the probability that the mean of private vehicles ages is between 3 to 9 years is 1.

b.) The probability that the mean of private vehicles ages is over 6 years is given by

Using the table of areas under the standard normal curve or a calculator, we have .

Therefore, the probability that the mean of private vehicles ages is over 6 years is 0.5.