Part 1 Of 9 Question 1 Of 2510 Points Suppose That A Histogr

Part 1 Of 9 Question 1 Of 2510 Pointssuppose That A Histogram Of A D

Suppose that a histogram of a data set is approximately symmetric and "bell shaped". Approximately, what percent of the observations are within three standard deviations of the mean? A.95% B.68% C.50% D.99.7%

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In statistical analysis, the properties of a bell-shaped, symmetric histogram often indicate a normal distribution. One of the key features of the normal distribution is the empirical rule, which describes how data values are spread around the mean. According to the empirical rule, approximately 95% of data points lie within two standard deviations of the mean, while about 99.7% of data points fall within three standard deviations. This rule is fundamental in probability and statistics, providing a clear understanding of variability in data that conforms to a normal distribution. Recognizing this pattern allows analysts to make predictions about data extent and to identify outliers effectively.

Given the options, the percentage of observations within three standard deviations from the mean, when the histogram is bell-shaped and symmetric, corresponds to roughly 99.7%. This is consistent with the empirical rule, which states that nearly all data under a normal curve falls within this range.

Therefore, the correct answer is D. 99.7%.

References

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