Respuesta :
Answer:
C. 0.403
Step-by-step explanation:
Binomial distribution has two parameter n and p. Here, n=15 and p=0.60.
We have to find the probability of 10 or more will show that the hamburger, French fries and a drink were ordered. P(X≥10)=?
The binomial probability distribution function for random variable X is
[tex]P(X=x)=nCxp^{x} q^{n-x}[/tex]
where q=1-p=1-0.6=0.4,n=15 and p=0.6.
P(X≥10)=P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)
[tex]P(X=10)=15C10(0.6^{10})( 0.4^{5})[/tex] =0.185938
[tex]P(X=11)=15C11(0.6^{11}) (0.4^{4})[/tex] =0.126776
[tex]P(X=12)=15C12(0.6^{12}) (0.4^{3})[/tex] =0.063388
[tex]P(X=13)=15C13(0.6^{13}) (0.4^{2})[/tex] =0.021942
[tex]P(X=14)=15C14(0.6^{14}) (0.4^{1})[/tex] =0.004702
[tex]P(X=15)=15C15(0.6^{15}) (0.4^{0})[/tex] =0.000470
P(X≥10)= 0.185938 +0.126776 +0.063388 +0.021942 +0.004702 +0.000470
P(X≥10)=0.403216
So, the probability of 10 or more will show that the hamburger, French fries and a drink were ordered is 0.403.
