The combined city/highway fuel economy of a 2016 Toyota 4Runner 2wd…

Question Answered step-by-step The combined city/highway fuel economy of a 2016 Toyota 4Runner 2wd… 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 8.8b. What sample size is needed to estimate the mean with 90 percent confidence and an error of 0.25mpg. Table 8.8:Four Ways to Estimate σMethod 1: Take a Preliminary SampleTake a small preliminary sample and use the sample estimate s in place of σ. This method is common, though its logic is somewhat circular (i.e., we must take a sample to plan a sample).Method 2: Assume Uniform PopulationEstimate upper and lower limits a and b and set σ = [(b − a )2/12]1/2. For example, we might guess the weight of a light-duty truck to range from 1,500 pounds to 3,500 pounds, implying a standard deviation of σ = [(3,500 − 1,500)2/12]1/2 = 577 pounds. Because a uniform distribution has no central tendency, the actual σ is probably smaller than our guess, so we get a larger n than necessary (a conservative result).Method 3: Assume Normal PopulationEstimate upper and lower bounds a and b, and set σ = (b − a)/6. This assumes normality with most of the data within μ + 3σ and μ − 3σ, so the estimated range is 6σ. For example, we might guess the weight of a light truck to range from 1,500 pounds to 3,500 pounds, implying σ = (3,500 − 1,500)/6 = 333 pounds. Recent research suggests that this method may not be conservative enough (see Related Reading).Method 4: Poisson ArrivalsIn the special case when λ is a Poisson arrival rate, then σ = √λ. For example, if you think the arrival rate is about 20 customers per hour, then you would estimate σ = √20 = 4.47. Math Statistics and Probability DAT/ 565 Share QuestionEmailCopy link Comments (0)