The waiting time at an elevator is uniformly distributed bet

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. A) Find the mean and standard deviation of the waiting time. B) If the waiting time is exponentially distributed, how does that change your answer?

Solution

a)

Note that here,          
          
a = lower fence of the distribution =    30      
b = upper fence of the distribution =    200      
          
Thus, the mean, variance, and standard deviations are          
          
u = mean = (b + a)/2 =    115   [ANSWER]

  
s^2 = variance = (b -a)^2 / 12 =    2408.333333      
s = standard deviation = sqrt(s^2) =    49.07477288   [ANSWER]

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b)

If it were exponentially distirbuted, the mean and standard deviations would be equal.