A car fleet of a delivery company consists of 145 cars.

Data recorded during the last month shows that the mean fuel consumption of cars is 6 liters per 100 km with standard deviation 1.4 liters and exhibit Uniform Distribution.

Assume this characteristic to be the population characteristics and they

do not change in time, and the fuel consumption of cars is stable. If 49 cars have been randomly selected for delivery today.....

a) what is the distribution of the average fuel consumption of the selected cars?

b) what is the probability that the average fuel consumption of the selected cars is less than 5.8 liters/100km ?

c) which value of average fuel consumption is such that in only 5% cases we get average fuel consumption of selected cars higher than this value?

d) At the end of day you have observed the average fuel consumption of the selected cars to be 7 liters,

what you can claim about the characteristics (mean and standard deviation) of your car fleet?

Any help you can provide with this problem would be greatly appreciated!