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 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 helpfiles for
Cross-tabs in the Basics menu and
Linear regression (OLS) in the Model menu for details.