5.1
Normal distribution curve
A continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve.
If a z-score is zero, which of the following must be true? Explain your reasoning. - The mean is zero. - The corresponding x-value is zero. - The corresponding x-value is equal to the mean.
The corresponding x-value is equal to the mean, because the z-score is equal to the difference between the x-value and the mean, divided by the standard deviation.
Are graphs that cross the x axis representative of a normal distribution?
The graph could not represent a variable with a normal distribution because the curve crosses the x-axis.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The mean and standard deviation have the values of mean= 0 and standard dev = 1
What do the inflection points on a normal distribution represent? Where do they occur?
They are the points at which the curve changes between curving upward and curving downward. Mean - Standard Dev and Mean + Standard Dev Outside of the inflection points, the graph curves upward.
Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences. The two curves will have ____ of symmetry. The curve with the larger standard deviation will be ____ spread out than the curve with the smaller standard deviation.
the same line, more
Why is it correct to say "a" normal distribution and "the" standard normal distribution?
"The" standard normal distribution is used to describe one specific normal distribution (mean = 0, standard dev = 1) . "A" normal distribution is used to describe a normal distribution with any mean and standard deviation.
In a normal distribution, which is greater, the mean or the median? Explain.
Neither; in a normal distribution, the mean and median are equal.
What is the total area under the normal curve?
1
