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?

Explanation

given

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

formula for the probability exponential distribution is given by

$\begin{gathered} P(x\leq a)=1-e^{-\frac{a}{\mu}} \\ P(aa) the mean is the reciprocal of the constant , so[tex]\mu=\frac{1}{0.50}=2$

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

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

c) probability of 1 minute or less between phone calls

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

d)

probability of 5 or more minutes without a phone call

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

Final Answer

Therefore ,

a) 2 minutes

b) 0.2212

c) 0.3935

d) 0.0821