Question

In a family with 3 children, the probability that all the children are girls is appoximately 0.125. In a random sample of 1000 families with 3 children, what is the approximate probability that 95 or fewer will have 3 girls? Approximate a binomial distribution with a normal distribution 囲Click the icon to view the area under the standard normal curve table. The probability that 95 or fewer families will have 3 girls is (Round to four decimal places as needed.)

Answer 1

Mean = np = 1000 * 0.125 = 125

Standard deviation = Sqrt (np(1-p))

= sqrt( 1000 * 0.125 * 0.875)

= 10.45825

Using normal approximation ,

P( X <= x) = P( Z < x+0.5 - mean / SD)

So,

P (X <= 95) = P( Z < 95.5 - 125 / 10.45825 )

= P( Z < -2.8207)

= 0.0024 (From Z table)