Answer the following questions and round your answers to 2 decimal places. 84% o
ID: 3306676 • Letter: A
Question
Answer the following questions and round your answers to 2 decimal places. 84% of all Americans live in cities with population greater than 50,000 people. If 50 Americans are selected at random, find the probability that
A. Exactly 42 of them live in cities with population greater than 50,000 people.
0.56
0.85
0.15
0.44
B. At most 45 of them live in cities with population greater than 50,000 people.
0.23
0.09
0.92
0.08
C. More than 40 of them live in cities with population greater than 50,00000 people.
0.11
0.89
0.27
0.73
D. Between 35 and 40 (including 35 and 40) of them live in cities with population greater than 50,000 people/
0.73
0.27
0.37
0.63
Explanation / Answer
Pr( Americans who live in the city with more than population of 50000) = 0.84
(1) Pr (X = 42 ; 50; 0.84) = BIN (X = 42 ; 50 ; 0.84) where n = 50 and p = 0.84
= 50C42 (42)0.84 (8)0.16 = 0.1523 (Option C)
(2) At most 45 will live in the cities
Pr(X <=45) = CBIN ( X <=45; 50; 0.84) ; cumulative Binomial
Pr(X <=45) = 0.9192 by binomial table
Option C is correct.
(3) Pr (X >- 40) = 1 - CBIN ( X<= 40; 50; 0.84) ; cumulative binomial
Pr(X <=40) = 0.7283
Pr (X >- 40) = 1 - 0.7283 = 0.2717 (Option C is correct)
(4) Pr(35 <= X <= 40 ; 50; 0.84) = CBIN(X <=40; 50; 0.84) - CBIN (X <35 ; 50; 0.84)
= 0.2718 - 0.0038 = 0.268 ( Option B is correct)
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