Respuesta :
Answer:
[tex]P(x\geq 7)=0.1886[/tex]
Step-by-step explanation:
The variable x, that said the number of customer that will order a nonalcoholic beverage in a sample of n customers follows a binomial distribution. Because we have n identical and independent events with a probability p of success and (1-p) of fail.
So, the probability that x customers will order a nonalcoholic beverage is:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]
Where n is the size of the sample and p is the probability that a customer order a nonalcoholic beverage, so replacing the values, we get:
[tex]P(x)=\frac{10!}{x!(10-x)!}*0.51^{x}*(1-0.51)^{10-x}[/tex]
Now, the probability that at least 7 will order a nonalcoholic beverage is equal to:
[tex]P(x\geq 7)=P(7)+P(8)+P(9)+P(10)[/tex]
Where:
[tex]P(7)=\frac{10!}{7!(10-7)!}*0.51^{7}*(1-0.51)^{10-7}=0.1267\\P(8)=\frac{10!}{8!(10-8)!}*0.51^{8}*(1-0.51)^{10-8}=0.0494\\P(9)=\frac{10!}{9!(10-9)!}*0.51^{9}*(1-0.51)^{10-9}=0.0114\\P(10)=\frac{10!}{10!(10-10)!}*0.51^{10}*(1-0.51)^{10-10}=0.0011[/tex]
So, [tex]P(x\geq 7)[/tex] is equal to:
[tex]P(x\geq 7)=0.1267+0.0494+0.0114+0.0011\\P(x\geq 7)=0.1886[/tex]
Finally, the probability that in a sample of 10 customers, at least 7 will order a nonalcoholic beverage is equal to 0.1886
