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