Question

a)Find the probability that of the next ten single births in a hospital in the district, eight or nine of them boys?

b)Find the probabiliyt that the next 15 single birth in a hospital in that district, more than one newborn is a boy?

c) Find the probability that of the next 20 single births in a hospital in the district, between 13 and 16 births are boys?

d)Find the probabiltiy that of the next 8 single births in a hospital in that districts the number of the boys is within one standard deviation of its mean.

Answer 1

p = 0.5

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

a)
P(X = 8) + P(X = 9)
= 10C8 * 0.5^8 * 0.5^2 + 10C9 * 0.5^9 * 0.5^1
= 0.0537

b)
P(X > 1)
= 1 - P(X <= 1)

P(X <= 1) = P(X = 0) + P(X = 1)
= 0.5^15 + 15C1 * 0.5^1 * 0.5^9
= 0.0005

P(X > 1) = 1 - 0.0005 = 0.9995

c)
P(13 <= X <= 16)
= P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)
= 0.1303