Question 855493
The expected value (E) is the mean of an exponential distribution
E[X] = 1 / lamda = 4000
lamda = 1 / 4000
f(x, lamda) = lamda * e^(-lamda*x)
note that e is equal to 2.71828
a) P(X>4500) = e^(-4500*lamda) = 2.71828^(-4500*1/4000)
 P(X>4500) = 0.32
b)P(4000 < X < 4750) = P(X>4000) - P(X>4750)
P(4000 < X < 4750) =  e^(-4000*lamda) - e^(-4750*lamda)
P(4000 < X < 4750) =   .37 - .30 = 0.07
c)P(X<3250) = 1 - P(X>3250)
P(X<3250) = 1 - e^(-3250*lamda)= 1 - 0.44 = 0.56