Question

1.

Mrs. Walker filled out a bracket for the NCAA National Tournament. Based on her knowledge of college basketball, she has a 0.53 probability of guessing any one game correctly.

What is the probability Mrs. Walker will pick all 32 of the first round games correctly?

What is the probability Mrs. Walker will pick exactly 10 games correctly in the first round?

What is the probability Mrs. Walker will pick exactly 20 games incorrectly in the first round?

2.

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only five women among the last 19 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.

Help her address the charge of gender discrimination by finding the probability of getting five or fewer women when 19 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).
P(at most five) =

thank you

Answer 1

#1) let x be the number of games guessed correctly .

x follows binomial distribution with n = 32 and p = 0.53

Binomial formula : P( x ) =

i) P( x = 32 )

= = 0.53³²

= 0

ii) P( x = 10 )

=

= 0.0069

iii) Now we are asked to find probability for exactly 20 games incorrectly , it means 32-20 = 12 games guessed correctly

So we have to find P( x = 12 )

=

= 0.0307

#2) Let x be the number of women are hired

x follows binomial distribution with n = 19 , p= 0.5 and q = 1-0.5 = 0.5

We are asked to find P( x ≤ 5 )

P( x ≤ 5 ) = P( x =0 ) + P( x =1 ) + P( x = 2 ) + P( x =3 ) + P( x =4 ) + P( x = 5 )

P( x =0 ) = = 0

P( x =1 ) = = 0

P( x =2 ) = = 0.0003

P( x = 3 ) = = 0.0018

P( x = 4 ) = = 0.0074

P( x =5 ) = =0.0222

P( x ≤ 5 ) = 0+0+0.0003+0.0018+0.0074+0.0222

P( x ≤ 5 ) = 0.0317