Question

A recent survey found that 70% of all adults over 50 wear glasses for driving. in a random sample of 12 adults over 50, what is the probability that at least seven wear glasses?

Answer 1

p(x) =   P^x q ^(n-x) x=0,1,.......n

p+q=1,0<p<1

n=12, p=0.70, q=0.30

p(x>=7)=1 - p(x<7)

=1 - binomcdf ( 12, 0.70 , 6 )

= 1- 0.1178

= 0.8821

OR

p(x>=7) = p(x=7) +p(x=8) + p(x=9) + p(x=10) + p(x=11) + p(x=12)

= (0.7)⁷  (0.3)⁵  + (0.7)⁸  (0.3)⁴  + (0.7)⁹  (0.3)³ + (0.7)¹⁰  (0.3)² +

(0.7)¹¹  (0.3)¹ + (0.7)¹²  (0.3)⁰

= 0.1584 +0.2311 + 0.2397 + 0.1678 +0.0712 + 0.0138

= 0.8820

The probability that at least seven wear glasses is 0.8820 i .e. 88.20 %