Data File 3
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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?
Answer: According to the 68-95-99.7:
* 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...
Show all work
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?
Answer: According to the 68-95-99.7:
* 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...