Answer:
a
[tex]\mu = 25 [/tex]
b
[tex]\lambda =0.04 [/tex]
c
[tex]P(X > 65 ) =0.0742 [/tex]
Step-by-step explanation:
From the question we are told that
The number of success is n = 5
The time duration is N = 125 minutes
Generally the mean of the random variable is mathematically represented as
[tex]\mu = \frac{N}{n}[/tex]
=> [tex]\mu = \frac{125}{5}[/tex]
=> [tex]\mu = 25 [/tex]
Generally the rate parameter is mathematically represented as
[tex]\lambda = \frac{1}{\mu}[/tex]
=> [tex]\lambda = \frac{1}{25}[/tex]
=> [tex]\lambda =0.04 [/tex]
Generally the cumulative distribution function for exponential distribution function is
[tex]F(x) = \left \{0 \ \ \ \ \ \ x \le 0}} \atop {1 -e^{-\lambda t }\ x>0}} \right.[/tex]
Generally the probability that the time to success will be more than 63 minutes is mathematically represented as
[tex]P(X > 65 ) = 1 - P(X \le 65)[/tex]
Here
[tex]P(X \le 65) = 1 -e^{-65 * \lambda }[/tex]
=> [tex]P(X \le 65) = 1 -e^{-65 * 0.04 }[/tex]
=> [tex]P(X \le 65) = 0.92573[/tex]
So
[tex]P(X > 65 ) = 1 - 0.92573 [/tex]
[tex]P(X > 65 ) =0.0742 [/tex]
