Miles per gallon. In its Fuel Economy Guide for 2014 model vehicles the Environm
ID: 3181559 • Letter: M
Question
Miles per gallon. In its Fuel Economy Guide for 2014 model vehicles the Environmental Protection Agency gives data on 1160 vehicles. There are a number of high outliers, mainly hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the combined 88 city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.2 miles per gallon (mpg) and standard deviation 5.2 mpg. Exercises 3.35 to 3.38 concern this distribution 3.35 I love my bug! The 2014 Volkswagen Beetle with a four-cylinder 1.8 L engine and automatic transmission has combined gas mileage of 28 mpg. What percent of all vehicles have better gas mileage than the Beetle? 3.36 The top 5%. How high must a 2014 vehicle's gas mile- age be to fall in the top 5% of all vehicles? 3.37 The middle half. The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. They span the middle half of the distribution. What are the quartiles of the distribution of gas mileage? 3.38 Quintiles. The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of gas mileage?Explanation / Answer
we are given that mean = 22.2 and sd = 5.2
3.35 )
we need to find P(X>28), so using the z tables and the z score formula we convert this X into a z score
as Z = X-mean/sd = (28-22)/5.2 = 1.15
so we need to check P(Z>1.15) , using the z tables we get
P ( Z>1.15 )=1P ( Z<1.15 )=10.8749=0.1251, hence close to 12.5% are better than Beetle
3.26 )
top 5% mean that z score is 1.644, check the value of 0.95 in z tables
so we must put this in the formula
Z = (X-mean)/sd
1.64*5.2 = X- 22.2
X = 1.64*5.2+22.2 = 30.7 , hence the mileage should be 30.7
Please note that we can answer onyly 1 question at a time , have answered 2 for you .