# The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

Apply the 68-95-99.7 rule to this questions.

## I believe the "68-95-99.7 rule" means the percentage of observations within 1-2-3 standard deviations from the mean.

Try to apply the rule to answer the given question.

## To apply the 68-95-99.7 rule, we need to calculate the range within 2 standard deviations of the mean.

Step 1: Calculate the range within 1 standard deviation:
One standard deviation from the mean accounts for approximately 68% of the data.

Lower limit: Mean - 1 standard deviation = 270 - 11 = 259
Upper limit: Mean + 1 standard deviation = 270 + 11 = 281

Step 2: Calculate the range within 2 standard deviations:
Two standard deviations from the mean account for approximately 95% of the data.

Lower limit: Mean - 2 standard deviations = 270 - (2 * 11) = 248
Upper limit: Mean + 2 standard deviations = 270 + (2 * 11) = 292

Therefore, approximately 95% of the light bulbs will have lifetimes that lie within 2 standard deviations of the mean (between 248 and 292 hours).

## To solve this question using the 68-95-99.7 rule, we need to identify the percentage of bulbs whose lifetimes lie within 2 standard deviations of the mean on either side.

According to the 68-95-99.7 rule:

- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.

Since we are interested in the bulbs whose lifetimes fall within 2 standard deviations, we can conclude that approximately 95% of the bulbs will have lifetimes within the range of (mean - 2 * standard deviation) to (mean + 2 * standard deviation).

Using the given mean of 270 hours and the standard deviation of 11 hours, we can calculate the range within which approximately 95% of the bulbs will lie:

Range = (270 - 2 * 11) to (270 + 2 * 11)

Simplifying this, we get:

Range = 248 to 292

Therefore, approximately 95% of the bulbs will have lifetimes that lie within the range of 248 hours to 292 hours.