Suppose that a histogram of a data set is approximately symmetric and "bell shaped". Approximately what percent of the observations are within one standard deviation of the mean?

Suppose that a histogram of a data set is approximately symmetric and "bell shaped". approximately what percent of the observations are within one standard deviation of the mean?

a. 99.7%

b. 50%

c. 68%

d. 95%

Option c is the right choice where, 68% of the observations are within 1 standard deviation.

Step-by-step explanation:

Given :

Standard deviation of the population = [tex]\sigma[/tex]

Average value for the population,(mean) = [tex]\mu[/tex]

Score or the data point to be converted = [tex]x[/tex]

So,

Z-score formula = [tex]\frac{x-\mu}{\sigma}[/tex]

If the Z-score is positive, it means the score is above the average value, whereas a negative Z-score indicates the score is below the average.

According to the question within 1 standard deviation (SD) of the mean is the [tex]\mu-\sigma[/tex] to [tex]\mu+\sigma[/tex] values from the bell shaped diagram.

One of a diagram is attached below.

And

The 68-95-99.7 Rule/Three sigma rule/Empirical rule states that, for normally distributed samples:

This rule is often used in statistics for forecasting.
68% of the measures are within one standard deviation of the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.

So,

Our final answer is of 68%,as of the measures are with in one SD.