Stats YEAR 2 Chapter 3

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Characteristics of a normal distribution curve

What does a normal distribution curve look like?

It looks like a bell shaped curve which is symmetrical on both sides. We usually draw the y axis where the mean is so we can represent the symmetry.

How does standard deviation affect the spread of the curve?

The greater the standard deviation the more spread out the curve will be, this tells us that the data recorded is more spread out. The lower the standard deviation the less spread out the curve will be and data values will be more close to the mean, this will tells us that the data recorded is not very spread out.

Normal distrubution equation.

If the variable is normally distributed we can use the normal distribution equation X~N(μ,σ²)

The parameter μ represents the mean of the population

The σ represents the standard deviation, which is squared (σ²) is the variance; the population variance.

Normal distribution facts

-The random variables have to be continuous

-The area under the curve has to add to a total of 1

-The y-axis represents probability density

-The probability that a continuous random variable takes 1 specific value is so small we say it is equal to 0

-The mean, mode and median for a normal distribution are all equal.

-It has points of inflection at μ±σ

-a

What is a continuous random variable and what is an discrete random variable, give an example of each.

A discrete variable is a variable which can only take a countable number of values. In this example, the number of heads can only take 4 values (0, 1, 2, 3) and so the variable is discrete. The variable is said to be random if the sum of the probabilities is one.

A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there are an infinite number of possible times that can be taken.