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enyata [817]
3 years ago
8

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?

Mathematics
1 answer:
patriot [66]3 years ago
4 0

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 = \sigma

Average value for the population,(mean) = \mu

Score or the data point to be converted = x

So,

Z-score formula = \frac{x-\mu}{\sigma}

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 \mu-\sigma to  \mu+\sigma 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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