Question

70% of all Americans are home owners. If 44 Americans are randomly selected, find the probability that

a. Exactly 30 of them are are home owners.
b. At most 32 of them are are home owners.
c. At least 32 of them are home owners.
d. Between 29 and 33 (including 29 and 33) of them are home owners.  

Answer 1

Solution:- Given that n = 44, p = 0.70

q = 1 - p = 1 - 0.7 = 0.3

a. P(X = 30) = 44C30*0.7^30*0.3^14 = 0.1239

b. P(X <= 32) = 0.7064

c. P(X >= 32) = 0.4173

d. P(29 <= X <= 33) = P(X = 29) + P(X = 30) + P(X = 31) + P(X = 32) + P(X = 33)
= 0.1062+0.1239+0.1306+0.1238+0.1050
= 0.5895