Name_____________________________________
LAB 5: Computing Binomial Probabilities
Purpose: In this lab, we will use Excel to solve problems using the binomial distribution (See Section 5.3
of the textbook for the binomial distribution). Open an Excel worksheet. Fill in the answers on this sheet
and turn it in.
Part I. Computing binomial probabilities. If x denotes a binomial random variable on n trials and
success probability p, then formula 5.5 on page 235 of the textbook gives: P(x) = nCx px qn-x, for
x=0,1,2,…,n (where q = 1-p). The command “=BINOMDIST(x,n,p,0)” in excel can be used to compute
these binomial probabilities.
Suppose x is a binomial random variable on n=5 trials and success probability p=0.3.
1. Compute P(x=2) by typing “=BINOMDIST(2,5,0.3,0)” in an empty cell in your excel worksheet.
Fill in the blank with your answer: P(x=2) = ____________________.
2. Compute P(x=4) = _____________________.
3. Compute the cumulative probability P(x ≤ 4) by typing “=BINOMDIST(4, 5, 0.3, 1)” in an empty
cell of your Excel worksheet. Note that to get a cumulative probability, simply change the “0” to
a “1” in the BINOMDIST function. P(x ≤ 4) = ___________________.
4. Use your answer from (3) to compute P(x > 4) = _______________ (hint: use Complement rule.)
Part II. Applying the Binomial distribution.
1. If x is binomial with n=50, p=0.9, use Excel to compute P(x ≤ 40) = _____________________.
2. A student takes a multiple choice test with 100 questions. Each question has 4 choices and
only one choice is correct. The student guesses the correct answer for each question. If
x=number of correct guesses, then x is a binomial random variable. Fill in the following
values:
a) n = _________, p = __________,  = ______________,  = _______________
b) To pass the test, the student must get 60 or more correct answers. What is the
probability the student passes? Note that by the law of complements :
P(x ≥ 60) = 1 – P(x ≤ 59). To get the answer, click in an empty cell and type “=1BINOMDIST(59,100,0.25,1)”. P(student passes) = _________________________.
3. Suppose there are 20 babies born at a small hospital and 200 babies born at a large hospital.
The probability that a baby is a girl is p= 0.50. Answer the following:
a) What is the probability that the number of girls born at the large hospital is 50 or
fewer? _____________________________________.
b) What is the probability that the number of girls born at the small hospital is 5 or
fewer? _____________________________________.
c) Which hospital is more likely to have only one-quarter or fewer of the babies be girls
(circle one): [Small hospital] [Large hospital] [Same probability for each hospital]