Question

Determine whether the variable X has a binomial distribution in each of the following cases. If it does, explain why and determine the values of the parameters n and p. If it doesn't, explain why not.

a) You toss five fair coins -- a loonie, a quater, a dime, a nickel and a penny.
X = number of coins that land on Heads

b) You select one row in the random digits Table B from the textbook.
X = number of 8's in the row

Answer 1

d) A fair die is repeatedly rolled.
X = number of rolls required to observe the number 5 for the third time.

Answer 2

c) You are dealt a five-card poker hand.


X = number of Diamonds in your hand.

Answer 3

You toss five fair coins -- a loonie, a quater, a dime, a nickel and a penny. X = number of coins that land on Heads
would certainly be binomial, as the outcomes of the tosses all have the same probability, and are independent
in this case \(p=1-p=\frac{1}{2}\) and \(n=5\)

Answer 4

very nice thanks, I just worked that out my self lol got the same answers tho. any ideas on the others?

Answer 5

for b) is this right?
the variable X has a binomial distribution because:
+ there is a fixed number of trials = 1 trials
+the outcome is number 8 or non-number 8
+its independent because whether you got 8 or not does not influence the next digits
+the probability is 10%
n= 1 p= 0.1