This is a question on a study guide for a test tomorrow. How do you do it? Please help
According to the Federal Highway Administration, teenage males drive an average of 10,718 miles each year. Assume the mileage totals are normally distributed with a standard deviation of 3573 miles. For a randomly selected teenage male, find the probability that he drives less than 9,000 miles in a year.
To find the probability that a randomly selected teenage male drives less than 9,000 miles in a year, we need to use the standard normal distribution.
1. Convert the problem to a standard normal distribution:
Since we know the population mean (μ = 10,718 miles) and the standard deviation (σ = 3,573 miles), we can convert the original problem into a standard normal distribution by using the formula:
z = (x - μ) / σ
In this case, we want to find the probability of driving less than 9,000 miles in a year, so x = 9,000 miles.
z = (9,000 - 10,718) / 3,573
= -0.482
2. Find the probability using a standard normal distribution table:
The standard normal distribution table provides the cumulative probability for each z-score, which represents the area under the curve to the left of the z-score.
Look for the z-score of -0.482 in the table. The closest value we can find is -0.4 (0.3446) and -0.5 (0.3085).
The difference between -0.482 and -0.5 is small, so we can estimate the probability as the average of the two probabilities:
P(z < -0.482) ≈ (0.3085 + 0.3446) / 2
≈ 0.3266
Therefore, the probability that a randomly selected teenage male drives less than 9,000 miles in a year is approximately 0.3266, or 32.66%.