Answer:
a
[tex]\mu  =  25 [/tex]
b
[tex]\lambda  =0.04 [/tex]
c
[tex]P(X > 65 ) =0.0742 Â [/tex] Â
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
 Â
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 Â
  [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] Â
=> Â Â Â [tex]P(X \le 65) = Â 1 -e^{-65 * Â 0.04 }[/tex] Â Â
=> Â Â Â [tex]P(X \le 65) = 0.92573[/tex] Â Â
So
   [tex]P(X > 65 ) =  1 - 0.92573 [/tex] Â
   [tex]P(X > 65 ) =0.0742  [/tex] Â
