Probability calculator
Calculate probabilities or values based on the Binomial, Chi-squared, Discrete, F, Exponential, Normal, Poisson, t, or Uniform distribution.
Suppose Consumer Reports (CR) wants to test manufacturer claims about battery life. The manufacturer claims that more than 90% of their batteries will power a laptop for at least 12 hours of continuous use. CR sets up 20 identical laptops with the manufacturer’s batteries. If the manufacturer’s claims are accurate, what is the probability that 15 or more laptops are still running after 12 hours?
The description of the problem suggests we should select
Binomial
from the Distribution
dropdown. To
find the probability, select Values
as the
Input type
and enter 15
as the
Upper bound
. In the output below we can see that the
probability is 0.989. The probability that exactly 15 laptops are still
running after 12 hours is 0.032.
A manufacturer wants to determine the appropriate inventory level for headphones required to achieve a 95% service level. Demand for the headphones obeys a normal distribution with a mean of 3000 and a standard deviation of 800.
To find the required number of headphones to hold in inventory choose
Normal
from the Distribution
dropdown and then
select Probability
as the Input type
. Enter
.95
as the Upper bound
. In the output below we
see the number of units to stock is 4316.
A discrete random variable can take on a limited (finite) number of possible values. The probability distribution of a discrete random variable lists these values and their probabilities. For example, probability distribution of the number of cups of ice cream a customer buys could be described as follows:
We can use the probability distribution of a random variable to calculate its mean (or expected value) as follows;
\[ E(C) = \mu_C = 1 \times 0.40 + 2 \times 0.30 + 3 \times 0.20 + 4 \times 0.10 = 2\,, \]
where \(\mu_C\) is the mean number of cups purchased. We can expect a randomly selected customer to buy 2 cups. The variance is calculated as follow:
\[ Var(C) = (1 - 2)^2 \times 0.4 + (2 - 2)^2 \times 0.3 + (3 - 2)^2 \times 0.2 + (4 - 2)^2 \times 0.1 = 1\,. \]
To get the mean and standard deviation of the discrete probability distribution above, as well as the probability a customer will buy 2 or more cups (0.6), specify the following in the probability calculator.
You can also use the probability calculator to determine a
p.value
or a critical value
for a statistical
test. See the help files for Single mean
,
Single proportion
, Compare means
,
Compare proportions
, Cross-tabs
in the
Basics menu and Linear regression (OLS)
in the
Model menu for details.
Add code to
Report
> Rmd to (re)create the analysis by clicking the
icon on the bottom
left of your screen or by pressing ALT-enter
on your
keyboard.
If a plot was created it can be customized using ggplot2
commands (e.g.,
plot(result) + labs(title = "Normal distribution")
). See
Data
> Visualize for details.
For an overview of related R-functions used by Radiant for probability calculations see Basics > Probability
Key functions from the stats
package used in the
probability calculator:
prob_norm
uses pnorm
, qnorm
,
and dnorm
prob_lnorm
uses plnorm
,
qlnorm
, and dlnorm
prob_tdist
uses pt
, qt
, and
dt
prob_fdist
uses pf
, qf
, and
df
prob_chisq
uses pchisq
,
qchisq
, and dchisq
prob_unif
uses punif
, qunif
,
and dunif
prob_binom
uses pbinom
,
qbinom
, and dbinom
prob_expo
uses pexp
, qexp
,
and dexp
prob_pois
uses ppios
, qpois
,
and dpois
Copy-and-paste the full command below into the RStudio console (i.e., the bottom-left window) and press return to gain access to all materials used in the probability calculator module of the Radiant Tutorial Series:
usethis::use_course("https://www.dropbox.com/sh/zw1yuiw8hvs47uc/AABPo1BncYv_i2eZfHQ7dgwCa?dl=1")
Describing the Distribution of a Discrete Random Variable (#1)
Describing Normal and Binomial Distributions in Radiant(#2)
Describing Uniform and Binomial Distributions in Radiant(#3)
Providing Probability Bounds(#4)