Question

SHOW WORK for both:

1. After examing her college attendance records for the past few years, Professor Bea Earlee
has determined that there is a 10% chance of any one student coming late to her class.
Eight students are randomly selected from her class rosters. Assuming her students arrive
to class independently of one another, what is the probability:

i) None of the eight students arrive late to class
ii) At most four students arrive late to class
iii) At least three students arrive late to class
iv) Exactly five students does NOT arrive late to class

2. After examing her college attendance records for the past few years, Professor Bea Earlee
has determined that there is a 10% chance of any one student coming late to her class.
Eight students are randomly selected from her class rosters. Assuming her students arrive
to class independently of one another, what is the probability:

i) None of the eight students arrive late to class
ii) At most four students arrive late to class
iii) At least three students arrive late to class
iv) Exactly five students does NOT arrive late to class

Answer 1

1 and 2 are the same

1) the probability that any one student coming late to her class is p = 0.1

n = 8  students are randomly selected from her class rosters

this is a binomial distribution

i) the probability that None of the eight students arrive late to class = ( using excel formula = BINOM.DIST(0,8,0.1,FALSE))
ii) the probability that at most four students arrive late to class:

( using excel formula =BINOM.DIST(4,8,0.1,TRUE))
iii) the probability that at least three students arrive late to class

( using formula =BINOM.DIST(2,8,0.1,TRUE)

iv) The probability that exactly five students does NOT arrive late to class =

This means that exactly 3 were late in the class

The probability that 3 of the eight students arrive late to class = ( using excel formula = BINOM.DIST(3,8,0.1,FALSE))