Question

EJERCICIO DE ESTADISTICAThe time (in minutes) between telephone calls at an insurance claims office has the exponential probability distributionf(x) = 0.50 e-0.50x for x ≥ 0.a. what is the mean time between phone calls?b. what is probability of 30 seconds or less between phone calls?c. what is probability of 1 minute or less between phone calls?d. what is probability of 5 or more minutes without a phone call?

Answer 1

Given

Exponential probability distribution

`f\mleft(x\mright)=0.50e^(-0.50x),x≥0.`

Find

a) what is the mean time between phone calls?

b) what is probability of 30 seconds or less between phone calls?

c) what is probability of 1 minute or less between phone calls?

d) what is probability of 5 or more minutes without a phone call?

Step-by-step explanation

given

`f\mleft(x\mright)=0.50e^(-0.50x),x≥0.`

formula for the probability exponential distribution is given by

b) probability of 30 seconds or less between phone calls is

`P(x\leq0.50)=1-e^{-(0.50)/(2)}\approx0.2212`

c) probability of 1 minute or less between phone calls

`P(x\leq1)=1-e^{-(1)/(2)}\approx0.3935`

d)

probability of 5 or more minutes without a phone call

`P(x\ge5)=e^{-(5)/(2)}\approx0.0821`

Final Answer

Therefore ,

a) 2 minutes

b) 0.2212

c) 0.3935

d) 0.0821