Question

6. There are 40 books on a bookshelf. Exactly 10 of them have a red cover. The remaining books have a white cover. You intend to choose a random sample of nine books, but you haven't decided whether to choose with replacement or without replacement?

a) If you choose books with our placement, would this procedure lead to independent trials or dependent trials?

b)if you choose books with replacement, would this procedure be consistent with a binomial experiment or not?

c) what is the size of the population? show your work

d) what is the size of the sample? show your work

e) if you ultimately conduct a binomial experiment, find the probability that the 5th book you select, happens to have a red cover? please show your work

f) if you ultimately conduct a binomial experiment, find the probability that you choose two or more red-covered books? please show your work

Finally, for a binomial experiment, please determine: show your work

1. average number of red books, per sample of nine books?
2. the variance of the number of red books, per sample of nine books?

Answer 1

(a)

If you choose books without replacement, this procedure would lead to dependent trials.

(b)

If you choose books with replacement, this procedure would be consistent with a binomial experiment.

(c)

the size of the population = 40, because it is given: There are 40 books on a bookshelf.

(d)

the size of the sample = 9, because it is given: You intend to choose a random sample of nine books

(e)

if you ultimately conduct a binomial experiment, the probability that the 5th book you select, happens to have a red cover = 10/40 = 0.25

(f)

if you ultimately conduct a binomial experiment, the probability that you choose two or more red-covered books :

n = 9

p = 10/40 = 0.25

q = 1 - p = 0.75

P(X2) =1 -[P(X=0) +P(X=1)]

Substituting, we get:

P(X2) =1 -[P(X=0) +P(X=1)] = 1 - 0.3003= 0.6997

So,

Answer is:

0.6997

(a)

average number of red books, per sample of nine books = np = 9 X0.25 = 2.25

(b)

the variance of the number of red books, per sample of nine books = npq= 9 X 0.25 X 0.75 = 1.6875