SOLUTION: HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! A random variable X is exponentially distributed with an expected value of 67. a-1. What is the rate parameter λ? (Roun

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Question 1163033: HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A random variable X is exponentially distributed with an expected value of 67.

a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)

a-2. What is the standard deviation of X?

b. Compute P(58 ≤ X ≤ 76). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

c. Compute P(55 ≤ X ≤ 79). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
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.