Respuesta :
Answer:
The probability that the flight does not arrive more than 5 minutes late is: [tex]0.25[/tex]
The probability that the flight arrives more than 10 minutes late is: [tex]0.50[/tex]
The expected flight time, in minutes, is: [tex]130[/tex]
Step-by-step explanation:
The probability density function for a continuous uniform random variable between 120 and 140 minutes is given by:
[tex]f(x) = \left \{ {{\frac{1}{140-120} \hspace {5} 120\leq x\leq 140 } \atop {0}\hspace {25} o.c.}\right.[/tex]
The probability that the flight does not arrive more than 5 minutes late is:
[tex]\int\limits^{130}_{125} {\frac{1}{20}} \, dx = \frac{1}{4} = 0.25[/tex]
The probability that the flight arrives more than 10 minutes late is:
[tex]\int\limits^{135}_{125} {\frac{1}{20}} \, dx = \frac{1}{2} = 0.50[/tex]
The expected flight time, in minutes, is:
[tex]\int\limits^{140}_{120} {\frac{x}{20}} \, dx = 130[/tex]
The probability of the flight will be no more than 5 and 10 minutes late are 0.25 and 0.5 respectively. The expected flight time is 130 minutes.
What is the probability density function?
It is used to define the random unknown probabilities coming within a distinct range of values, is open to taking on anyone's value.
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa.
Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.
The probability density function for a continuous uniform random variable between 120 and 140 minutes is given as
[tex]f(x)=\left\{\begin{matrix} \dfrac{1}{140-120}, 120\leq x\leq 140\\\\0, o.e \end{matrix}\right.[/tex]
The probability that the flight will be no more than 5 minutes late will be
[tex]\rm \int _{125}^{130} \dfrac{1}{20} dx = \dfrac{1}{20} (5) = \dfrac{1}{4} = 0.25[/tex]
The probability that the flight will be no more than 10 minutes late will be
[tex]\rm \int _{125}^{135} \dfrac{1}{20} dx = \dfrac{1}{20} (10) = \dfrac{1}{4} = 0.5[/tex]
The expected flight time, in minutes, will be
[tex]\rm \int _{120}^{140} \dfrac{x}{20} dx = \dfrac{5200}{2*20} (5) = \dfrac{260}{20} = 130[/tex]
More about the probability density function link is given below.
https://brainly.com/question/14749588
