Answer:
a)[tex]P(6)=0.25[/tex]
b)[tex]p(x<g)=0.9537[/tex]
c)[tex]p(x\geq3)=0.9878[/tex]
d)[tex]\sigma=\sqrt{2.4}=1.5492[/tex]
Explanation:
From the question we are told that:
Population percentage [tex]p_\%=\60%[/tex]
Sample size [tex]n=10[/tex]
Let x =customers ask for water
Let y =customers dose not ask for water with their meal
Generally the equation for y is mathematically given by
[tex]y=1-p_\%\\y=1-0.60\\y=0.40[/tex]
Generally the equation for pmf p(x) is mathematically given by
[tex]P(x)=10C_x (0..6)^x(0.4)^{10-x}[/tex]
a)
Generally the probability that exactly 6 ask for water is mathematically given by
[tex]P(x)6=10C_6 (0..6)^6(0.4)^{10-6}[/tex]
[tex]P(6)=0.25[/tex]
b)
Generally the probability that less than 9 ask for water with meal is mathematically given by
[tex]p(x<g)=1-p(x>g)[/tex]
[tex]p(x<g)=1(p(9))+p(10)[/tex]
[tex]p(x<g)=1-(10_C_9 (0..6)^9(0.4)^{10-9}+10_C_10 (0..6)^10(0.4)^{10-10})\\p(x<g)=1-0.0463[/tex]
[tex]p(x<g)=0.9537[/tex]
c)
Generally the probability that at least 3 ask for water with meal is mathematically given by
[tex]p(x\geq3)=1-p(x<3)[/tex]
[tex]p(x\geq3)=1-[p(0)+p(1)+p(2)][/tex]
[tex]p(x\geq3)=1-[0.00001+0.0015+0.0106][/tex]
[tex]p(x\geq3)=1-[0.0122][/tex]
[tex]p(x\geq3)=0.9878[/tex]
d)
Generally the mean and standard deviation of sample size is mathematically given by
Mean
[tex]\=x=np=10(0.6)=6[/tex]
Standard deviation
[tex]v(x)=npq=10(0.6)(0.4)=2.4[/tex]
[tex]\sigma=\sqrt{2.4}=1.5492[/tex]
