Suppose that a histogram of a data set is approximately symmetric and "bell shaped". Approximately what percent of the observati
ons are within one standard deviation of the mean?
1 answer:
Answer:
<em>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? </em>
<em>a. 99.7% </em>
<em>b. 50% </em>
<em>c. 68% </em>
<em>d. 95%</em>
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 =
Average value for the population,(mean) =
Score or the data point to be converted =
So,
Z-score formula =
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 to
values from the bell shaped diagram.
<em>One of a diagram is attached below.</em>
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.
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