Question

Average age of vehicle registaion in the U.S is 8 yrs ( 96 months). Assume stand dev. of 16 months.

(a) If a randpm sample of 36 vehicles are selected, find probability their mean age is between 90 & 100 months.
(b) find probability a random vehicle has mean age between 90 & 100 months.

Answer 1

To solve this problem, we will use the Central Limit Theorem since we have a large sample size. We need to find the probability that the mean age of a random sample of 36 vehicles is between 90 and 100 months, as well as the probability that a random vehicle has a mean age between 90 and 100 months.

Step-by-step explanation:

To solve this problem, we will use the Central Limit Theorem since we have a large sample size.

(a) To find the probability that the mean age of a random sample of 36 vehicles is between 90 and 100 months, we need to standardize the values using the z-score formula. The z-score formula is z = (x - μ) / (σ / sqrt(n)), where x is the mean age of the sample, μ is the population mean, σ is the population standard deviation, and n is the sample size. Once we have the z-scores, we can look up the corresponding probabilities in the standard normal distribution table or use a calculator.

(b) To find the probability that a random vehicle has a mean age between 90 and 100 months, we can use the same formula as in part (a) and calculate the z-score for a single vehicle.