Respuesta :
Answer:
- m = [tex]\frac{1}{20}[/tex]
- μ = 20
- σ = 20
The probability that a person is willing to commute more than 25 miles is 0.2865.
Step-by-step explanation:
Exponential probability distribution is used to define the probability distribution of the amount of time until some specific event takes place.
A random variable X follows an exponential distribution with parameter m.
The decay parameter is, m.
The probability distribution function of an Exponential distribution is:
[tex]f(x)=me^{-mx}\ ;\ m>0, x>0[/tex]
Given: The decay parameter is, [tex]\frac{1}{20}[/tex]
X is defined as the distance people are willing to commute in miles.
- The decay parameter is m = [tex]\frac{1}{20}[/tex].
- The mean of the distribution is: [tex]\mu=\frac{1}{m}=\frac{1}{\frac{1}{20}}=20[/tex].
- The standard deviation is: [tex]\sigma=\sqrt{variance}= \sqrt{\frac{1}{(m)^{2}} } =\frac{1}{m} =\frac{1}{\frac{1}{20}} =20[/tex]
Compute the probability that a person is willing to commute more than 25 miles as follows:
[tex]P(X>25)=\int\limits^{\infty}_{25} {\frac{1}{20} e^{-\frac{1}{20}x}} \, dx \\=\frac{1}{20}|20e^{-\frac{1}{20}x}|^{\infty}_{25}\\=|e^{-\frac{1}{20}x}|^{\infty}_{25}\\=e^{-\frac{1}{20}\times25}\\=0.2865[/tex]
Thus, the probability that a person is willing to commute more than 25 miles is 0.2865.
