Question

Suppose that a certain car model has gas milage rated at 27mpg (mean) with a standard deviation of 3mpg. A certain rental car company owns 60 of these cars. Answer the following questions, showing each step of your work and summarizing your results with a sentence of the form: "There is a x% probability that the mean milage for the (randomly selected) fleet of 60 cars is at least/at most y mpg." 1. What is the probability that the mean milage of this fleet of cars is at least 26.5 ?

Answer 1

There is a 9.85% probability that the mean mileage for the fleet of 60 cars is at least 26.5 mpg.

Step-by-step explanation:

To find the probability that the mean mileage of the fleet of cars is at least 26.5 mpg, we need to calculate the z-score for this value and then find the corresponding probability using a z-table.

The formula to calculate the z-score is:

z = (x - μ) / (σ / √n)

where x is the given value, μ is the mean, σ is the standard deviation, and n is the sample size.

In this case, x = 26.5 mpg, μ = 27 mpg, σ = 3 mpg, and n = 60.

Substituting the values into the formula:

z = (26.5 - 27) / (3 / √60) = -0.5 / 0.387 = -1.29

Looking up the z-score -1.29 in the z-table, we find that the corresponding probability is 0.0985.

Therefore, there is a 9.85% probability that the mean mileage for the fleet of 60 cars is at least 26.5 mpg.