The car’s owners manual said that it had a 10-gallon gas tank. You kept track of the number of gallons of gas

needed to fill up the tank once the “Low Fuel” icon lit up on the dashboard. Here are the results of 20 randon fill-ups (in-gallons): 10.27, 10.15, 10.18, 10.05, 10.08, 10.11, 10.12, 10.29, 10.10, 10.19, 9.96, 10.14 10.16, 10.29, 10.23, 10.19, 10.10, 10.33, 10.06, 10.18

(a) Let X represent the number of gallons of gas needed to fill your car’s gas tank. In order to

use the formula from the lesson to construct a confidence interval for the true mean number of gallons of gas μ to fill your gas tank, we have to assume that  is normally distributed. Why is this a reasonable assumption based on the boxplot and histogram? Please note that this question is asking about the shape of  x-bar  and not X.