Respuesta :
Answer:
a)0.074
b)0.502
c)0.2114
d)0.0166
e)0.01790
f)0.9987
Step-by-step explanation:
Probability of being left handed = 0.13
Probability of being not left handed = 1-0.13 =0.87
They select a sample of five customers at random in their stores
a. The first lefty is the fifth person chosen
Probability that first lefty is the fifth person chosen =[tex]0.87 \times 0.87 \times 0.87 \times 0.87 \times 0.13=0.074[/tex]
b)There are some lefties among the 5 people=[tex]1-P(x=0)=1-0.87^5=0.502[/tex]
c)The first lefty is the second or third person=[tex]0.87 \times 0.13 + 0.87 \times 0.87 \times 0.13 =0.2114[/tex]
d)
[tex]P(x=3)=^5C_3 (0.13)^3 (0.87)^2=\frac{5!}{3!2!}(0.13)^3 (0.87)^2=0.0166[/tex]
e)
[tex]P(x\geq 3)=P(x=3)+P(x=4)+P(x=5)\\P(x\geq 3)=\frac{5!}{3!2!}(0.13)^3 (0.87)^2+\frac{5!}{4!1!}(0.13)^4(0.87)^1+\frac{5!}{5!0!}(0.13)^5 (0.87)^0=0.01790[/tex]
f)
[tex]P(x\leq 3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)[/tex]
[tex]P(x\leq 3)=\frac{5!}{0!5!}(0.13)^0 (0.87)^5+\frac{5!}{4!1!}(0.13)^1(0.87)^4+\frac{5!}{2!3!}(0.13)^2 (0.87)^3+\frac{5!}{2!3!}(0.13)^3 (0.87)^2=0.9987[/tex]
