Question 1163033
E(X)=1/ lambda=67
so lambda, the rate parameter, is 1/67 or 0.0149

variance is (1/lambda^2), so sd is 1/lambda or also 67 

The mean and the sd are the same

The density function is lambda e^(-lambda x)

p(x < 76)=is  1-e^(-.0149*76)=0.6784.  I used 1-e^(-76/67)
p( x <58)= 1-e^(.0149*58)=0.5792
The probability of being in that range is the difference or 0.0991 (I used the fraction 1/67 and then rounded)

p(x < 79) is 1-e^(-79/67)=0.6924
p( x < 55) is 1- e^(-55/67)=0.5600
and that difference is 0.1324 and the probability of the interval desired.