The values of x-axis that are one, two and three standard deviations away from the mean are plotted in the given graph.
One can use empirical rule for normal distribution and the fact that the normal distribution is symmetric to its mean, and that its bell shaped.
Using the percentage given by empirical rule, we get the average idea of how much area is to be kept under what interval of values.
According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
where we had where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex]
For the given case, let the random variable be X whose data has to be plotted.
From the given information, we get: [tex]X \sim N(\mu = 15, \sigma = 4)[/tex]
Using the empirical rule we get that,
[tex]P(26< X <34) = 68\%\\P(22 < X < 38) = 95\%\\P(18 < X <42) = 99.7\%[/tex]
These probabilities can correspond to area too. 68% of area is between 26 and 34 values, and so on for obtained intervals.
We get the graph as attached graph below.
Learn more about normal distribution here:
https://brainly.com/question/15395456
