http://www.ck12.org Chapter 4. Standard Distributions - Basic
Notice that when we actually flipped the 100 coins in our experiment, we saw that tails come up 70 times and heads
only 30 times. The theoretical probability is what we would expect to happen. In a regular fair coin toss, we have
an equal chance of getting a head or a tail. Therefore, if we flip a coin 100 times we would expect to see 50 heads
and 50 tails. When we actually flip 100 coins, we actually saw 70 tails and 30 heads. If we were to repeat this
experiment, we might see 60 tails and 40 heads.
If we were to keep doing this flipping experiment, say 500 times, we may see the values get closer to the theoretical
probability (the histogram on the left). As the number of data values increase, the graph of the results starts to look
a bell-shaped curve. This type of distribution of data is normal orstandard distribution. The distribution of the data
values is shown in this curve. The more data points, the more we see the bell shape.
Between the two red lines represents 68% of the data. Between the two purple lines represents 95% of the data.
Between the two blue lines represents 99.7 % of the data. You will learn more about the normal distribution in
Chapter 5.
What is interesting about our flipping coin example is that it is a binomial experiment. What is meant by this is that
it does not have a standard distribution but a binomial distribution. Why? This is because binomial experiments
only have two outcomes. Think about it. If we flip a coin, choose between true or false, choose between a Mac
or a PC computer, or even asked for tea or coffee at a restaurant, these are all options that involve either one
choice or another. These are all experiments that are designed where the possible outcomes are either one or the
other.Binomial experimentsare experiments that involve only two choices and their distributions involve a discrete
number of trials of these two possible outcomes. Therefore abinomial distributionis a probability distribution of
the successful trials of the binomial experiments.
Technology Note
Let’s try the following on the graphing calculator. We are going to flip a coin 15 times and count the number of
heads. Now, remember, the probability of getting a head is 50%. We are then going to repeat this experiment 25
times. On the graphing calculator, press the following: