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 continuos use. CR sets up 20 identical laptops with the manufacturerâ€™s batteries. If the manufacturerâ€™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:

- 40% of customers buy 1 cup;
- 30% of customers buy 2 cups;
- 20% of customers buy 3 cups;
- 10% of customers buy 4 cups.

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 helpfiles 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.