Binomial and Normal Distribution Characteristics
The characteristics of the binomial and normal distributions: a fixed number of trials with two outcomes, the symmetric bell shape, the empirical rule of about 68 and 95 out of 100, and quality assurance action and warning lines.
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Two important distributions
Statisticians often meet two shapes of data again and again. The binomial distribution counts successes in a fixed number of tries, and the normal distribution is the smooth bell shape that so many real measurements follow. This module sets out what each one looks like and how it is used. Note that this is Higher-tier content.
Distribution vocabulary
Learn these four terms before you study the shapes.
Binomial or normal
The two distributions describe different kinds of data.
Tell them apart
A top answer names the right shape. The binomial is a count of successes over a fixed number of tries with two outcomes each time. The normal is the smooth bell curve where most values sit near the mean. For the normal, remember the rule of thumb about how the data clusters: most readings lie within one or two standard deviations either side of the middle, and anything far beyond that is very unusual.
Match the term
- binomial distribution
- normal distribution
- standard deviation
- symmetric
- a count of successes in fixed tries
- the smooth bell-shaped curve
- how spread out the values are
- the same on both sides of the middle
Match the feature
- two outcomes each try
- a fixed number of tries
- a bell-shaped curve
- mean, median and mode together
- a feature of the binomial distribution
- another feature of the binomial distribution
- a feature of the normal distribution
- another feature of the normal distribution
Which is normal?
Which description fits a normal distribution?
- A smooth, symmetric bell shape.
- A count of successes in a few tries.
- A shape leaning heavily to one side.
- A completely flat line.
Binomial features
Select the TWO features of a binomial distribution.
- A fixed number of tries.
- Two outcomes on each try.
- A smooth bell-shaped curve.
- Any value on a continuous scale.
Order the quality check
Put the steps of a quality assurance check in order, earliest first.
- Take a sample from the production line
- Plot the value on the control chart
- If it passes a warning line, watch closely
- If it passes an action line, stop and adjust
Complete the facts
A count of successes in a fixed number of tries is the _____ distribution. The smooth bell-shaped curve is the _____ distribution, which is _____ about its mean. About 68 out of 100 values lie within one _____ of the mean. On a control chart, a value beyond the _____ line means stop and adjust.
Outside two deviations
In a normal distribution about 95 out of every 100 values lie within two standard deviations of the mean. Subtract 95 from 100 to find how many out of 100 lie outside that range. What is the answer?
True of the normal
Tap the TWO statements that are true of a normal distribution.
- it is symmetric about the mean
- it has a bell shape
- it counts successes in fixed tries
- it has only two possible outcomes
Name the distribution
Read each situation and choose the best answer.
- A coin is flipped 5 times and the number of heads is counted. Which distribution fits?
- The heights of many adults form a smooth, symmetric bell shape. Which distribution fits?
- A sample on a control chart falls beyond the action line. What should happen?
Describe the distributions
Describe the characteristics of the binomial and normal distributions and how they differ.
- Describe the binomial distribution and when it is used
- Describe the normal distribution and its bell shape
- State the rule about 68 and 95 out of 100 for the normal distribution