Answer:
The probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.
Step-by-step explanation:
The random variable X is defined as the amount of time until the next student will arrive in the library parking lot at the university.
The random variable X follows an Exponential distribution with mean, μ = 4 minutes.
The probability density function of X is:
[tex]f_{X}(x)=\lambda e^{\lambda x};\ x\geq 0, \lambda >0[/tex]
The parameter of the exponential distribution is:
[tex]\lambda=\frac{1}{\mu}=\frac{1}{4}=0.25[/tex]
Compute the value of P (X > 10) as follows:
[tex]P(X>10)=\int\limits^{\infty}_{10}{0.25e^{-0.25x}}\, dx[/tex]
[tex]=0.25\times \int\limits^{\infty}_{10}{e^{-0.25x}}\, dx\\=0.25\times |\frac{e^{0.25x}}{-0.25}|^{\infty}_{10}\\=(e^{-0.25\times \infty})-(e^{-0.25\times 10})\\=0.0821[/tex]
Thus, the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.
