Question

In a rural area of South Carolina, 49 percent of adults are in favor of passing law XYZ. If 27 adults are randomly selected, what is the probability of exactly 19 being in favor of XYZ?  

  a. 0.013   b. 0.023 c. 0.033 d. 0.043

What is the probability of at least 17 being in favor of law XYZ (see question 8 above)?  

a. 0.204       b. 0.304 c. 0.404 d. 0.104

9. What is the probability of at least 17 being in favor of law XYZ (see question 8 above)?  

a. 0.204       b. 0.304 c. 0.404 d. 0.104

Answer 1

8.

By using binomial distribution

P ( X )

= ( n c x ) p x q n - x

= ( 27 C 19 ) ( 0.49 ) 19 ( 0.51 ) 27 - 19

= 0.013

So the option is ( a )

9.

P ( X )

= ( n c x ) p x q n - x

= ( 27 C 17 ) ( 0.49 ) 17 ( 0.51 ) 27 - 17 + ( 27 C 18 ) ( 0.49 ) 18 ( 0.51 ) 27 - 18 + ( 27 C 18 ) ( 0.49 ) 18 ( 0.51 ) 27 - 18  + ( 27 C 19 ) ( 0.49 ) 19 ( 0.51 ) 27 - 19  + ( 27 C 20 ) ( 0.49 )20  ( 0.51 ) 27 - 20 + ( 27 C 21 ) ( 0.49 ) 21 ( 0.51 ) 27 - 21 + ( 27 C 22) ( 0.49 ) 22( 0.51 ) 27 - 22  + ( 27 C 23 ) ( 0.49 ) 23 ( 0.51 ) 27 - 23 + ( 27 C 24) ( 0.49 ) 24 ( 0.51 ) 27 - 24 + ( 27 C 25 ) ( 0.49 ) 25( 0.51 ) 27 - 25 + ( 27 C 26 ) ( 0.49 ) 26 ( 0.51 ) 27 - 26 + ( 27 C 27 ) ( 0.49 ) 27 ( 0.51 ) 27 - 27

= 0.204

So the option is ( a )