Statistics problem

Question

Each person has a 75% probability of going to the Ches Tahoe restaurant. a. You randomly select 8 people. What is the probability that 5 people will not go to the restaurant? b. You randomly select 50 people. Use normal approximation to find the probability that at least 35 people will go to the restaurant.

Answer 1

P(c) = .75

8 people are chosen at random

P(5 of the 8 will not go) could mean probability exactly 5 will not go which means exactly 3 will go

or it might mean at least 5 will not go. >5 or =5

which means the probability that at most 3 will go, =3 or <3

P(exactly 5 will not go)

= P(exactly 3 will go)

= 8C3(.25)^5(.75)^3

=8C3(1/4)^5(3/4)^3

= 8!/3!5!(1/1024)(27/64)

= [8(7)(6)/3(2)](27/65536)

=1512/65536

= about 2.3%

P(at least 5 will not go)

= P(5)+P(6)+P(7) + P(8)

= .023 + 8C6(.25)^6(.75)^2 + 8C7(.25)^7(.75) + 8C8(.25)^8