Binomial Distributions Worksheet 1
You may wish to use the interactive binomial
probabilities page. This page duplicates and expands
on the binomial tables. (Opens in a separate browser
window.)
P1. For a binomial variable X, with n
= 5 and p = 0.40.
 Use the cumulative probabilities (tabled) to find
f(x) = P[ X = x ] for each possible value of X.
 Draw a histogram.
 Compute the mean and standard deviation of X.
Locate the mean on the horizontal axis your
histogram.
P2. For a binomial variable X, with n
= 14 and p = 0.80, find
 P[ X <= 8 ]. (<= is the "less than or
equal to" sign)
 P[ X = 8 ].
 P[ X >= 12 ].
 The mean and standard deviation of X.
 P[ 9 <= X <= 13 ].
P3. For the binomial distribution
with n = 10 and p = 0.3, find the probability of
 Five or more successes.
 At most two successes.
 At least one success.
 At least 50% successes.
P4. Find the probability of
 12 successes in 20 trials when the probability of
a success is 0.7.
 8 failures in 20 trials when the probability of a
failure is 0.3.
 Explain why you get identical answers in parts
(a) and (b).
P5. The population of a large city is
60% AfricanAmerican. A jury of 12 is selected at random
from the citizens of the city.
 What is the probability that at most 3
AfricanAmericans are selected?
 What is the probability that at most 2
AfricanAmericans are selected?
 What is the expected number of AfricanAmericans
on the jury? What is the standard deviation?
P6. Suppose, for the purpose of
argument, that 20% of the otters in a large aquatic
community are infected with a parasite. A biologist
samples 16 otters at random and records, for each,
whether or not the animal is infected.
 Find the mean number of infected otters in the
sample.
 What is the probability exactly 20% of the
sampled otters are infected?
 What is the probability more than 50% of the
sampled otters are infected? To get a better feel
for this probability, compute its reciprocal.
 Suppose more than 50% of the sampled otters are
infected. How might the biologist respond to such
information? Use the probability of part (d) to
support your argument.
P7. When an assembly machine is
properly calibrated approximately 5% of the finished
products are defective. Periodically the quality control
engineer randomly selects 20 products at random, and
tests them. He will halt the production line to check
(and reconfigure, if necessary) the calibration if any of
the tested products are defective. Assuming that the
machine is properly calibrated, what is the probability
that production must be halted?
