Practice Binomial distribution
A binomial distribution counts successes in a fixed number of independent trials with the same success probability.
Check these assumptions before using its formula.
Exercises with solutions
A binomial distribution applies when a random experiment is repeated n times, there are only two outcomes (hit and miss), the probability of a hit p stays the same in every trial and the trials are independent. Then μ = n · p and σ = √(n · p · (1 − p)).
Exercise 1
A die is rolled 60 times; a six counts as a hit. What is the expected number of hits?
Show solution and working
10
With n = 60 and p = 1/6, μ = 60 · 1/6 = 10.
Exercise 2
What is the standard deviation in this example?
Show solution and working
about 2.89
σ = √(60 · 1/6 · 5/6) = √(50/6) ≈ √8.33 ≈ 2.89.
Exercise 3
Why may you not use the binomial distribution when drawing without replacement?
Show solution and working
because the trials are not independent
Without replacement the probability of a hit changes after every draw, so one requirement of the binomial distribution is violated.
Exercise 4
What does a sigma interval describe?
Show solution and working
a range around the expected value
In the interval μ ± 2σ about 95 % of the results lie for a binomial distribution.
Common mistake
Using the binomial distribution although the probability of a hit is not constant, for instance when drawing without replacement. And swapping n and p.
Keep learning with MatheJump
Create a free account and explore math practice. Choose from the available exercises to suit your learning needs.