Statistics problem

Question

1. What is the range of fuel efficiency for cars within 1σ of the mean? a. 24 mpg – 34 mpg b. 28 mpg – 30 mpg c. 29 mpg – 34 mpg d. −1 mpg – +1 mpg
2. What percent of all cars get less than 20 mpg? a. 31.0% b. 3.6% c. 5.5% d. 50%
3. What percent of all cars get between 22 and 32 mpg? a. 64.5% b. 68.8% c. 60.1% d. 34.5
4. Describe the fuel efficiency of the worst 25% of all cars. a. Cars in the lower 25% of the left tail average less than 21.8 mpg. b. Cars in the lower 25% of the left tail average less than 19.6 mpg. c. Cars in the lower 25% of the left tail average less than 25.6 mpg. d. Cars in the lower 25% of the left tail average less than 23.5 mpg.
5. What gas mileage represents the third quartile? a. 26.4 mpg b. 31.2 mpg c. 32.4 mpg d. 33.2 mpg

Answer 1

I can edit this answer once a mean and standard deviation are provided. If this is not a normal distribution (highly unlikely), I'll edit a lot on this answer

1) To get that range that is within 1 standard deviation of the mean, simply use the formula μ±σ.

2, 3) For these you'll want to find the z score corresponding to the value (20 for (2) and 22 and 32 for (3)). The z score formula is z=(X-μ)/σ, where X is the value you're looking at. Then you'd look at this value on a z-score table. For 3, you'll be finding two left-tail areas and finding the difference between these.

Alternatively, if you have a TI-84 or the like, you can use the normalCDF function to solve these. For 2, your lower bound would be 0 and upper bound would be 20. For 3, your bounds are obviously 22 and 32.

4, 5) Here you're doing the reverse process of 2 and 3; look up 0.25 and 0.75 on the z-table, and use that to find your cutoff value. Using the same z score formula above, we could get X=μ+zσ. The z scores for the two problems would be -0.675 and 0.675 for these two problems.