Please help!The scheduled commuting time on the shuttle "LX" from the student center to library is 15 minutes. Suppose that the actual commuting time is uniformly distributed between 10 and 22 minutes.(a) What is the probability that the commuting time will be less than 13 minutes?(b) What is the probability that the commuting time will be between 12 and 18 minutes?(c) What are the expected commuting time and the standard deviation of the commuting time?(d) How much can the expected commuting time be decreased if the actual commuting time isuniformly distributed between 10 and 20 minutes?

Answer:Step-by-step explanation:Let X be the scheduled commuting time on the shuttle "LX" from the student center to library is 15 minutes.Suppose that the actual commuting time is uniformly distributed between 10 and 22 minutes.X is U(10,22)a)  the probability that the commuting time will be less than 13 minutes=[tex]\frac{13-10}{22-10} =0.25[/tex]b)  the probability that the commuting time will be between 12 and 18 minutes =[tex]\frac{18-12}{22-10} =0.50[/tex]c)  the expected commuting time=E(x) = [tex]\frac{10+22}{2} =16[/tex] the standard deviation of the commuting time=Std dev (x) = [tex]\sqrt{\frac{22^2-10^2}{144} } =0.6667[/tex]d) the expected commuting time be decreased if the actual commuting time is  uniformly distributed between 10 and 20 minutesNew mean = [tex]\frac{10+20}{2} =15[/tex]I.e. mean reduced by 1 minute.