Question

The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 20.50 mpg and a standard deviation of σ = 3.00 mpg What is the standard error of X¯¯¯X¯ , the mean from a random sample of 36 fill-ups by one driver?

Answer 1

The standard error of the mean fuel economy for a random sample of 36 fill-ups of a 2016 Lexus RX 350 is 0.50 mpg.

Step-by-step explanation:

The standard error of the mean, ¡X¯, in a normally distributed random variable is calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). In the case of the 2016 Lexus RX 350 with a mean fuel economy (μ) of 20.50 mpg and a population standard deviation (σ) of 3.00 mpg for a random sample of 36 fill-ups, the standard error (σ_X¯) can be computed as follows:

σ_X¯ = σ / √n

σ_X¯ = 3.00 mpg / √36

σ_X¯ = 3.00 mpg / 6

σ_X¯ = 0.50 mpg

Therefore, the standard error of the mean fuel economy for the given sample is 0.50 mpg.