The binomial distribution table** **is a table that shows probabilities associated with the binomial distribution. To use the binomial distribution table, you only need three values:

**n:**the number of trials**r:**the number of “successes” during n trials**p:**the probability of success on a given trial

Using these three numbers, you can use the binomial distribution table to find the probability of obtaining exactly **r **successes during **n **trials when the probability of success on each trial is **p**.

The following examples illustrate how to read the binomial distribution table.

**Example 1**

**Question: **Jessica makes 60% of her free-throw attempts. If she shoots 6 free throws, what is the probability that she makes exactly 4?

To answer this question, we can look up the value in the binomial distribution table that corresponds to **n **= 6, **r **= 4, and **p **= 0.60:

The probability that Jessica makes exactly 4 out of 6 free throws is **0.311**.

**Example 2**

**Question: **Jessica makes 60% of her free-throw attempts. If she shoots 6 free throws, what is the probability that she makes less than 4?

To find this probability, we actually have to add up the following probabilities:

P(makes less than 4) = P(makes 0) + P(makes 1) + P(makes 2) + P(makes 3)

So, we can look up each of these four probabilities in the binomial distribution table and add them up:

According to the table, P(makes less than 4) = .004 + .037 + .138 + .276 = **0.455**.

The probability that Jessica makes less than 4 free throws is **0.455**.

**Example 3**

**Question: **Jessica makes 60% of her free-throw attempts. If she shoots 6 free throws, what is the probability that she makes 4 or more?

To find this probability, we have to add up the following probabilities:

P(makes 4 or more) = P(makes 4) + P(makes 5) + P(makes 6)

So, we can look up each of these three probabilities in the binomial distribution table and add them up:

According to the table, P(makes 4 or more) = .311 + .187 + .047 = **0.545**.

The probability that Jessica makes 4 or more free throws is **0.545**.

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