Answer:
[tex]P(X\geq 8)=0.0043\\\\[/tex]
It's more likely that all of the residents surveyed will have adequate earthquake supplies since it has a probability of 98.02% which is very close to 100%.
Step-by-step explanation:
-This is a binomial probability problem with the function:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]
-Given p=0.3, n=11, the is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)+P(X=11)\\\\={11\choose 8}0.3^8(0.7)^3+{11\choose 9}0.3^9(0.7)^2+{11\choose 10}0.3^{10}(0.7)^1+{11\choose 11}0.3^{11}(0.7)^0\\\\=0.0037+0.0005+0.00005+0.000002\\\\=0.0043[/tex]
Hence, the probability that at least 8 have adequate supplies 0.0043
#The probability that non has adequate supplies is calculated as;
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= 0)={11\choose 0}0.3^{0}(0.7)^{11}\\\\=0.0198[/tex]
#The probability that all have adequate supplies is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= All)=1-{11\choose 0}0.3^{0}(0.7)^{11}\\\\=1-0.0198\\\\=0.9802[/tex]
Hence, it's more likely that all of the residents surveyed will have adequate earthquake supplies since [tex]P(All)>P(None)\ \[/tex] and that this probability is 0.9802 or 98.02% a figure close to 1
