Question

fill in the blanks with an appropriate word, phrase, or symbol(s).

according to the empirical rule, in a normal distribution, approximately ____% of the data lie within plus or minus 1 standard deviation of the mean, approximately __% of the data lie within plus or minus 2 standard deviations of the mean, and approximately ____% of the data lie within plus or minus 3 standard deviations of the mean.

Explanation:

Identify the standard percentages of the empirical rule

The empirical rule (also known as the 68-95-99.7 rule) states that for a normal distribution:

• Approximately \(68\%\) of the data lie within plus or minus 1 standard deviation of the mean.
• Approximately \(95\%\) of the data lie within plus or minus 2 standard deviations of the mean.
• Approximately \(99.7\%\) of the data lie within plus or minus 3 standard deviations of the mean.

Match the values to the blanks in the sentence

The sentence is:
"According to the empirical rule, in a normal distribution, approximately [Blank 1]% of the data lie within plus or minus 1 standard deviation of the mean, approximately [Blank 2]% of the data lie within plus or minus 2 standard deviations of the mean, and approximately [Blank 3]% of the data lie within plus or minus 3 standard deviations of the mean."

• Blank 1 corresponds to 1 standard deviation: \(68\)
• Blank 2 corresponds to 2 standard deviations: \(95\)
• Blank 3 corresponds to 3 standard deviations: \(99.7\)

Answer:

According to the empirical rule, in a normal distribution, approximately <blank>68</blank>% of the data lie within plus or minus 1 standard deviation of the mean, approximately <blank>95</blank>% of the data lie within plus or minus 2 standard deviations of the mean, and approximately <blank>99.7</blank>% of the data lie within plus or minus 3 standard deviations of the mean.