Question

A set of data with a mean of 53, and a standard deviation of 6.2 is normally distributed. Find the value of a data point that is -2 standard deviations from the mean.

Answer 1

The value of a data point that is -2 standard deviations from the mean

so, 40.6 to 65.4.

What is the empirical rule?

According to the empirical rule, also known as the 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.

$P(\mu - \sigma < X < \mu + \sigma) \approx 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%$

From the empirical rule, we know that for 95% we are in 2 standard deviations of the mean. so:

= 53- 6.2- 6.2

= 40.6

The value of a data point that is -2 standard deviations from the mean

53 + 6.2 + 6.2

= 65.4

Learn more about the empirical rule here:

brainly.com/question/13676793

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