Question

64% of all Americans live in cities with population greater than 100,000 people. If 38 Americans are randomly selected, find the probability that

a. Exactly 24 of them live in cities with population greater than 100,000 people._____
b. At most 25 of them live in cities with population greater than 100,000 people._____
c. At least 22 of them live in cities with population greater than 100,000 people. _____
d. Between 22 and 27 (including 22 and 27) of them live in cities with population greater than 100,000 people._____

*** Enter an integral or decimal number.

Answer 1

Solution: Given that p = 0.64, n = 38

a. P(X = 24) = 38c24*0.64^24*0.36^14 = 0.1324

b. P(X <= 25) = 0.6497

c. P(X >= 22) = 0.8301

d. P(22 <= X <= 27) = P(22)+P(23)+P(24)+P(25)+(26)+P(27)
= 0.0964+0.1192+0.1324+0.1318+0.1172+0.0926
= 0.6896