A car manufacturer estimates that the gas mileage of their SUV models has a mean of 27.5 mpg and a standard deviation of 2.6 mpg for highway driving. Assume that the distribution is unimodal and symmetric. a. Find the mpgs for one and two standard deviations above and below the mean. (5 pts) b. Based on the Empirical Rule, between what two values would you expect to find 95% of the mpgs? (3 pts) c. What measure would be preferred for measuring the variability of the data set? (2 pts)
Added by Walter N.
Close
Step 1
5 + 2.6 = 30.1 mpg One standard deviation below the mean = 27.5 - 2.6 = 24.9 mpg Show more…
Show all steps
Your feedback will help us improve your experience
Jen H and 96 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The Normal distribution below models the distribution of highway gas consumption (in miles per gallon) for a large collection of SUVs when driving on level roads. The centre is shown at 24.8 mpg and the standard deviations reflect the spread of the data. (a) Find the standard deviation so that the top 2.5% of SUVs get 37.2 mpg or higher. (b) What percentage of SUV's consume less than 19 miles per gallon?
Joanna Q.
A new line of cars has gas mileage represented by a distribution that is approximately normal with a mean of 32 mpg and a standard deviation of 4 mpg. Use the empirical rule to answer the following: a) Approximately what percent of cars get between 24 and 32 mpg? b) Approximately what proportion of cars get between 28 and 40 mpg?
Narayan H.
In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 32 mpg and a standard deviation of 1.7 mpg. Suppose that the car manufacturer samples five cars from its assembly line and tests them for mileage ratings. a. What is the distribution of the mean mpg for the sample? b. What is the probability that the mean mpg of the sample will be greater than 34 mpg? c. What is the probability that the mean mpg of the sample will be less than 30.5 mpg?
Rosina D.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD