# Data File 3

Data File 3
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Chapter Five

1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

* Approximately 68% of light bulbs have a life between µ-σ = 2000 and µ+σ = 3000
(where µ is the mean and σ is the standard deviation)
* Approximately 95% of light bulbs have a life between µ-2σ = 1500 and µ+2σ = 3500
*   Approximately 99.7% of light bulbs have a life between µ-3σ = 1000 and µ+3σ = 4000

Therefore, (99.7%)/2= 49.85% of light bulbs have a life inferior to 2500 (which is the mean)

This result can be verified by using z score tables.   Indeed, µ=2500 and σ = 500

For the value 2500 hours,

Z score = 2500-2500500 = 0. The z score table reveals that the corresponding percentile is 50%.   Thus, 50% of light bulbs have a life less than   2500 hours

2) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?

Answer: µ = 370 hours and σ = 5 hours.   According to the 68-95-99.7 rule,
approximately 68% of light bulbs have a life within 1 standard deviation of the mean(µ) on either side, which is between µ-σ = 365 hours and µ+σ = 375 hours.   This result can be verified by using z score tables.

* Indeed, For the value µ+σ= 375, Z score = Value-MeanStandard Deviation = 375-3705 = 1

The z score table reveals that the corresponding percentile is 84.13%.

* For the value µ-σ = 365, Z score = Value-MeanStandard Deviation = 365-37010 = -1

The z score table reveals that the corresponding percentile is 15.87%

Thus, the percent of all scores that fall between µ-σ and µ+σ is (84.13...