The binompdf and binomcdf are two commands in a TI calculator that can be used to calculate probabilities associated with the binomial distribution.

A binomial distribution has two parameters ‘n’ which is the number of trials and ‘p’ which is the probability of success in a particular trial.

- The function binompdf(n, p, x) accepts the value of the n and p and tells you the probability that there are exactly x number of successes in ‘n’ trials. This basically means that this function outputs the probability mass function of the binomial random variable.
- The function binomcdf(n, p, x) accepts the value of the n and p and tells you the probability that there are less than or equal to x number of successes in ‘n’ trials. This basically means that this function outputs the cumulative distribution function of the binomial random variable.

**Example of binompdf command:**

Suppose that an archer tries to hit a target 7 times. It is known that the archer succeeds in hitting the target 35% of the time. Calculate the probability that the archer hits exactly 4 targets out of 7.

**Solution**: We are given n=7 and p=probability of success = 35% = 0.35

We want to find the probability of **exactly 4** successes therefore we use the command binompdf(7,0.35,4).

Click on 2^{nd} on the TI calculator and then click on DISTR which gives displays a list of distributions. Scroll down to reach the binompdf() command.

Input the values of n, p, and x given above and press enter. We get an output that looks like

Therefore we conclude that there is a 14.42% chance that the archer hits exactly 4 targets out of 7.

**Example of binomcdf command:**

Suppose that an archer tries to hit a target 7 times. It is known that the archer succeeds in hitting the target 35% of the time. Calculate the probability that the archer hits less than or equal to 4 targets out of 7.

**Solution**: We are given n=7 and p=probability of success = 35% = 0.35

We want to find the probability of **less than or exactly 4** successes therefore we use the command binomcdf(7,0.35,4).

We click on 2^{nd} on the TI calculator and then click on DISTR and scroll down to reach the binomcdf() command.

We input the values of n, p, and x given above and press enter. We get an output that looks like

Therefore we conclude that there is a 94.43% chance that the archer hits less than or equal to 4 targets out of 7.