Respuesta :
Answer:
The probability that the person retired after age 70 is 0.1353.
Step-by-step explanation:
The random variable X is defined as the time (in years) after reaching age 60 that it takes an individual to retire.
The random variable X follows an Exponential distribution with mean, β = 5 years.
The parameter of the exponential distribution is:
[tex]\lambda=\frac{1}{\beta}=\frac{1}{5}=0.20[/tex]
The probability distribution of an Exponential distribution is:
[tex]f(x)=\lambda e^{-\lambda x};\ x>0[/tex]
It is provided that a person retired after age 70 years.
Then the number of years after the retirement age is, 70 - 60 = 10 years.
Compute the probability of (X > 10) as follows:
[tex]\int\limits^{\infty}_{10} {\lambda e^{-\lambda x}} \, dx =\lambda |\frac{e^{-\lambda x}}{-\lambda}|^{\infty}_{10}=e^{-0.20\times10}-0=0.1353[/tex]
Thus, the probability that the person retired after age 70 is 0.1353.
