Respuesta :
Answer:
The mean and standard deviation of the number of cars recovered after being stolen is 522 and 8.24 respectively.
Step-by-step explanation:
We are given that according to insurance records, a car with a certain protection system will be recovered 87% of the time.
Also, 600 stolen cars are randomly selected.
Let X = Number of cars recovered after being stolen
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=01,2,3,......[/tex]
where, n = number of trials = 600 cars
r = number of success
p = probability of success which in our question is the probability
that car with a certain protection system will be recovered,
i.e. p = 87%.
So, X ~ Binom(n = 600, p = 0.87)
Now, the mean of X, E(X) = [tex]n \times p[/tex]
= [tex]600 \times 0.87[/tex] = 522
Also, the standard deviation of X, S.D.(X) = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{600 \times 0.87 \times (1-0.87)}[/tex]
= 8.24
