It has been determined that 30% of students at a certain high school own a cell phone. If 95 students are randomly selected determine the probability that exactly 20 students own a cell phone. *if using a calculator show syntax used*

To determine the probability that exactly 20 students own a cell phone, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:
P(X = k) represents the probability of getting exactly k successes,
C(n, k) represents the number of combinations of choosing k items from a set of n items, and
p represents the probability of getting a success on a single trial.

In this problem, we have n = 95 (the number of trials or students selected), p = 0.3 (the probability that a randomly selected student owns a cell phone), and k = 20 (the desired number of successes).

Using a standard scientific calculator or a statistical software program can be helpful for the calculations. If using a calculator, the syntax may vary depending on the specific calculator model.

Here's an example using a TI-84 calculator:

1. Press the MATH button.
2. Scroll right to the PRB menu (press the right arrow key).
3. Scroll down to binompdf( and press ENTER.
4. Enter the values inside the parentheses: binompdf(n, p, k).
- In this case, n = 95, p = 0.3, and k = 20. So, enter binompdf(95, 0.3, 20).
5. Press ENTER to calculate the probability.

The calculator will display the probability as a decimal value. For example, if the calculator shows 0.1002209874, it means the probability is approximately 0.1002 (rounded to four decimal places) or 10.02% (rounded to two decimal places).