High School

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean of 35.9 mpg and a standard deviation of 2.5 mpg.

a. What is the probability that a randomly selected passenger car gets more than 37 mpg? (Round your final answer to 4 decimal places.)

Answer :

Final answer:

The probability that a randomly selected passenger car gets more than 37 mpg is 33.00%. This calculation requires converting the mpg value to a z-score and consulting a z-table or standard normal distribution calculator.

Explanation:

In order to solve this problem, you'll need to convert the mpg value to a z-score, then use a z-table or a standard normal distribution calculator to find the probability. A z-score is a standard measurement that tells how many standard deviations a particular value is from the mean.

Step 1: Calculate the z-score. The formula for a z-score is (X - μ) / σ. In this case, X = 37 mpg, μ (the mean) = 35.9 mpg, and σ (the standard deviation) = 2.5 mpg. So, the z-score is (37 - 35.9) / 2.5 = 0.44.

Step 2: Look up the z-score in the z-table to find the probability. The value for 0.44 in the z-table is 0.6700, which represents the probability that a car gets less than or equal to 37 mpg. Because you want to find the probability that a car gets more than 37 mpg, you need to subtract this number from 1. So, the probability that a car gets more than 37 mpg is 1 - 0.6700 = 0.3300, or 33.00%.

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