Question

A survey report states that 60% of adult women visit their doctors for a physical examination at least once in two years. If 10 adult women are randomly selected, find the probability that:

(a) Exactly half of them have had a physical examination in the past two years.

(b) Fewer than 2 of them have had a physical examination in the past two years.

(c) The number of women who have had a physical examination in the past two years will be more than 3 and fewer than 8.

(d) More than 8 women have had a physical examination in the past two years.

Answer 1

a)
P(X = 5)
= 10C5 * 0.6^5 * 0.4^5
= 0.2007

b)
P(X < 2)
= P(X = 0) + P(X = 1)
= 0.4^10 + 10*0.6*0.4^9
= 0.0017

c)
P(X > 3 and X < 8)
= P(X = 4) + P(X = 5) + P(X = 6) + P(x = 7)
= 10C4 * 0.6^4 * 0.4^6 + 10C5 * 0.6^5 * 0.4^5 + 10C6 * 0.6^6 * 0.4^4 + 10C7 * 0.6^7 * 0.4^3
= 0.7779

d)
P(X > 8)
= P(X = 9) + P(X = 10)
= 10C9 * 0.6^9 * 0.4^1 + 0.6^10
= 0.0464