Respuesta :
Answer:
Probability that all 15 pay in cash is 1.074 [tex]\times 10^{-6}[/tex] .
Step-by-step explanation:
We are given that Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 15 customers
r = number of success = all 15
p = probability of success which in our question is % of all
customers who pay in cash, i.e; 40%
LET X = Number of customers who pay in cash
So, it means X ~ [tex]Binom(n=15, p=0.40)[/tex]
Now, Probability that all 15 customers who buy gasoline at this station pay in cash is given by = P(X = 15)
P(X = 15) = [tex]\binom{15}{15} \times 0.40^{15} \times (1-0.40)^{15-15}[/tex]
= [tex]1 \times 0.40^{15} \times 0.60^{0}[/tex]
= [tex]0.40 ^{15}[/tex] = 1.074 [tex]\times 10^{-6}[/tex]
Therefore, Probability that all 15 customers pay in cash is 1.074 [tex]\times 10^{-6}[/tex] .
