3) 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 17 mpg to 22 mpg. (a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution) from Table 8.8. (Round your answer to 4 decimal places.) (b) What sample size is needed to estimate the mean with 90 percent confidence and an error of ± 0.25 mpg? (Enter your answer as a whole number. Use a z-value taken to three decimal places in your calculations.)

4)Analysis showed that the mean arrival rate for vehicles at a certain Shell station on Friday afternoon last year was 4.5 vehicles per minute. How large a sample would be needed to estimate this year's mean arrival rate with 98 percent confidence and an error of ± 0.5? (Round the standard deviation answer to 4 decimal places. Enter your answer as a whole number. Use a z-value taken to four decimal places in your calculations.)

5)The EPA city/hwy mpg range for a Saturn Vue FWD automatic 5-speed transmission is 20 to 28 mpg. Use Method 3 from Table 8.8.

(a) Estimate σ using Method 3 from Table 8.8. (Round your answer to 4 decimal places.)
(b) If you owned this vehicle, how large a sample (e.g., how many tanks of gas) would be required to estimate your mean mpg with an error of ±1 mpg and 90 percent confidence? (Enter your answer as a whole number (no decimals). Use a z-value taken to three decimal places in your calculations.)

8) Find the interval [ μ− z σn√,μ+ z σn√ ]
within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.

(a) μ = 200, σ = 12, n = 36. (Round your answers to 2 decimal places.)

(b) μ = 1,000, σ = 15, n = 9.

10)The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000672 mm. Assume a random sample of 56 sheets of metal resulted in an x¯
= .2737 mm.

Calculate the 98 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.)