Assume that a normal distribution of data has a mean of 14 and a standard deviation of 4. Use the 68-95-99.7 rule to find the percentage of values that lie below 2.

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Answer :

TaylorSmith4590 TaylorSmith4590 · Answer 1 · 2025-02-25T06:04:51-05:00

Approximately 0.15% of the values lie below 2.

We need to determine how many standard deviations below the mean 2 is, and then use the 68-95-99.7 rule.

First, let's calculate how many standard deviations below the mean 2 is:

[tex]\[ \text{Number of standard deviations} = \frac{\text{value} - \mu}{\sigma} = \frac{2 - 14}{4} = \frac{-12}{4} = -3 \][/tex]

Since 2 is 3 standard deviations below the mean, we know from the 68-95-99.7 rule that:

- Approximately 99.7% of the data falls within three standard deviations below and above the mean.

- Therefore, approximately 0.15% of the data falls below three standard deviations below the mean.

So, approximately 0.15% of the values lie below 2.