Respuesta :
Answer:
The probability that exactly 30% of these 10 telephone users do not have landlines in their homes is 0.2668.
Step-by-step explanation:
We are given that a recent survey found that 30% of telephone users have switched completely to cell phone use (i.e. they do not have landlines in their homes).
A random sample of 10 of these customers is selected.
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 = 0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 10 customers
r = number of success = 30% of 10 = 3
p = probability of success which in our question is the probability
that telephone users do not have landlines in their homes,
i.e. p = 30%
Let X = Number of telephone users who do not have landlines in their homes
So, X ~ Binom(n = 10, p = 0.30)
Now, the probability that exactly 30% of these 10 telephone users do not have landlines in their homes is given by = P(X = 3)
P(X = 3) = [tex]\binom{10}{3}\times 0.30^{3} \times (1-0.30)^{10-3}[/tex]
= [tex]120 \times 0.30^{3} \times 0.70^{7}[/tex]
= 0.2668
