Graphical Analysis In Exercises 11–16, determine whether the g...

Question

Graphical Analysis In Exercises 11–16, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

dist1

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says, could this graph represent a variable with a normal distribution? If so, estimate the mean and standard deviation. If not, explain your reasoning. And below the text we're given a graph. Where our curve begins around X equals 232, it increases up to a maximum value of around X equals 234, and then it decreases again down to the initial starting value around X equals to 39. So, for the first part of this problem, we need to determine whether this graph represents a variable with a normal distribution. So recall for a normal distribution that it should be symmetric about its mean. Also, we call for a normal distribution that the mean occurs whenever a curve has reached its maximum value. So, if we look at the curve that we have here, the maximum value occurs around X equal to 34. And if we look at the curve to the part of the curve that is to the left of our peak here, we see that we begin around X equal to 32 and our function rises very rapidly to the peak. But to the right of X equals to 34, our curve here falls off gradually. So this means that the curve here is skewed to the right, which means it has a longer tail on the right side, which also means that it is not symmetric. And since our curve here is not symmetric, that means it is not a normal distribution, since a normal distribution must be symmetric. So that means that the answer to this question is no. And for our explanation, we see that our curve here is not symmetric. And it is also skewed. To the right. So it's not symmetric, and it is right skewed. That is going to be the answer. To this problem. So I hope that this explanation has been useful, and I'll see you in the next video.

Graphical Analysis In Exercises 11–16, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Key Concepts

Normal Distribution

Mean and Standard Deviation

Graphical Analysis

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