A transportation engineer is studying the distribution of fuel efficiencies (measured in miles per gal- lon,...

A transportation engineer is studying the distribution of fuel efficiencies (measured in miles per gal- lon, or mpg) for vehicles registered in Franklin county. Let Y denote the efficiency of a vehicle in mpg. The researcher models vehicle efficiency as following a normal distribution (i.e., the popula- tion distribution is normal) and randomly samples n = 16 vehicles from the population. The sample mean is y ̄ and the sample standard deviation is s. Answer the following questions. (If the exact values you need to solve these problems are not available in the appropriate table, use the closest values that are available.)

(a) Assume that the population mean of the efficiencies is μ = 30 but that the population stan- dard deviation is unknown. The calculated sample standard deviation is s = 5. What is the probability that the sample mean is within 2.5 mpg of the population mean?

(b) Estimate the mean efficiency in such a way that the accuracy is 1 mpg. Find the sample size (n) required to ensure that sample mean is within 1 mpg of the population mean with probability 0.90. Assume that the population standard deviation is known to be σ = 5.30.

(c) Assume that the population mean of efficiency is μ = 30 and the population standard deviation is known to be σ = 5.30. What is the probability that the sample standard deviation s is greater than 4?

Expert Solution

orchestra answered 2 years ago

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