Question

67% of all Americans live in cities with population greater than 100,000 people. If 35 Americans are randomly selected, find the probability that

a. Exactly 21 of them live in cities with population greater than 100,000 people.  
b. At most 22 of them live in cities with population greater than 100,000 people.
c. At least 24 of them live in cities with population greater than 100,000 people.  
d. Between 17 and 22 (including 17 and 22) of them live in cities with population greater than 100,000 people.

Answer 1

This is a case of binomial distribution with n = 35 and p = 0.67

We know that,

P(X=x) = (nCx)px(1-p)n-x

A.

P(X=21) = 0.0938

B.

P(X22) = 0.3598

C.

P(X24) = 0.5011

D.

P(17X22) = P(X22) - P(X<17)

= 0.3598 - 0.0076

= 0.3522

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