Question

The combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range 19 mpg to 22 mpg.

(a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution) from Table 8.11. (Round your answer to 4 decimal places.)
  
Standard deviation =

(b) What sample size is needed to estimate the mean with 95 percent confidence and an error of ± 0.25 mpg? (Enter your answer as a whole number (no decimals). Use a z-value taken to 3 decimal places in your calculations.)
  
Sample size =

Answer 1

Given that, the combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range 19 mpg to 22 mpg.

Range = 22 - 19 = 3

a) According to Empirical rule,

Standard deviation = Range / 4 = 3/4 = 0.75

=> Standard deviation (sd) = 0.75

b) Margin of error (E) = 0.25

A 95% confidence level has significance level of 0.05 and critical value is,

We want to find, the sample size (n),

=> Sample size = 35