A **uniform distribution** is a probability distribution in which every value between an interval from *a *to *b *is equally likely to be chosen.

The probability that we will obtain a value between x_{1} and x_{2} on an interval from *a *to *b *can be found using the formula:

P(obtain value between x_{1} and x_{2}) = (x_{2} – x_{1}) / (b – a)

The uniform distribution has the following properties:

- The mean of the distribution is
**μ**= (a + b) / 2 - The variance of the distribution is
**σ**= (b – a)^{2}^{2}/ 12 - The standard deviation of the distribution is
**σ**= √σ^{2}

**Examples: Uniform Distribution in Excel**

**Example 1: ***A bus shows up at a bus stop every 20 minutes. If you arrive at the bus stop, what is the probability that the bus will show up in 8 minutes or less?*

**Solution:**

- a: 0 minutes
- b: 20 minutes
- x
_{1}: 0 minutes - x
_{2}: 8 minutes

The probability that the bus shows up in 8 minutes or less is **0.4**.

**Example 2:***The weight of a certain species of frog is uniformly distributed between 15 and 25 grams. If you randomly select a frog, what is the probability that the frog weighs between 17 and 19 grams?*

**Solution:**

- a: 15 grams
- b: 25 grams
- x
_{1}: 17 grams - x
_{2}: 19 grams

The probability that the frog weighs between 17 and 19 grams is** 0.2**.

**Example 3: ***The length of an NBA game is uniformly distributed between 120 and 170 minutes. What is the probability that a randomly selected NBA game lasts more than 150 minutes?*

**Solution:**

- a: 120 minutes
- b: 170 minutes
- x
_{1}: 150 minutes - x
_{2}: 170 minutes

The probability that a randomly selected NBA game lasts more than 150 minutes is **0.4**.

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