Respuesta :
Answer: a. P (x<30) = 0.5276
b. P (30<x<35) = 0.0555
Step-by-step explanation: An exponential distribution is a distribution of time in which events happens at a constant average rate.
The rate is calculated as
[tex]\lambda=\frac{1}{\mu}[/tex]
with μ as the mean.
The probability density distribution for this type of distribution is
[tex]f(x)=\lambda e^{-\lambda x}[/tex]
And probability is calculated as
[tex]P(X<x)=1-e^{-\lambda x}[/tex]
For tuning of an engine, the rate is
[tex]\lambda=\frac{1}{40}[/tex]
λ = 0.025
a. Probability of less than 30 minutes:
[tex]P(X<30)=1-e^{-0.025.30}[/tex]
[tex]P(X<30)=1-e^{-0.75}[/tex]
P (X < 30) = 0.5276
Probability of tuning in 30 minutes or less is 52.76%.
b. Probability of between 30 and 35 can be described as
[tex]P(30<X<35)=P(X<35)-P(X<30)[/tex]
[tex]P(X<35)=1-e^{-0.025*35}[/tex]
[tex]P(X<35)=1-e^{-0.875}[/tex]
P (X < 35) = 0.5831
P (X < 30) = 0.5276
Then:
[tex]P(30<X<35)=0.5831-0.5276[/tex]
P (30 < X < 35) = 0.0555
Probability of tuning an engine between 30 and 35 minutes is 5.55%.
