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In a normal distribution, 68% of the data fall within how many standard
deviations of the mean?
A. Two standard deviations
B. One standard deviation
C. It cannot be determined from the given information.
D. Three standard deviations

Respuesta :

cmarsh1998
B, my teacher just taught us this :)

In a normal distribution of data, 68% of the data fall within one standard deviations of the mean.

What do you mean by normally distributed data?

Normally distributed data is the distribution of probability which is symmetric about the mean.

  • The mean of the data is the average value of the given data.
  • The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

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]

Here the mean of distribution of X is [tex]\mu[/tex]  and standard deviation from mean of distribution of X is [tex]\sigma[/tex].

Thus, in a normal distribution of data, 68% of the data fall within one standard deviations of the mean.

Learn more about the normally distributed data here;

https://brainly.com/question/6587992

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