Respuesta :
Given Information:
The average bulb life = μ = 600 hours
standard deviation = σ = 53 hours
Sample follows Bell-Shaped Distribution or Normal Distribution
Step-by-step explanation:
According to the Empirical Rule, 99.7% of the lightbulbs have lifetimes between μ - 3σ and μ + 3σ
600 - 3(53) and 600 + 3(53)
441 and 759 hours
(b) assuming the data are bell shaped, determine the percentage of lightbulbs that will have a life between 494 and 706 hours.
494 = 600 - 106 = 600 - 2(53) = μ - 2σ
706 = 600 + 106 = 600 + 2(53) = μ + 2σ
Therefore, according to the Empirical Rule, 95% of the lightbulbs have lifetimes between μ - 2σ and μ + 2σ
(c) Assuming the data are bell shaped, what percentage of lightbulbs will last between 547 and 706 hours?
547 = 600 - 53 = 600 - 1(53) = μ - σ
653 = 600 + 53 = 600 + 1(53) = μ + σ
Therefore, according to the Empirical Rule, 68% of the lightbulbs have lifetimes between μ - σ and μ + σ
(d) If the company that manufactures the lightbulbs guarantees to replace any bulb that does not last at least 441 hours, what percentage of lightbulbs can the firm expect to have to replace, according to the Empirical Rule?
441 = 600 - 159 = 600 - 3(53) = μ - 3σ
99.7% of the lightbulbs have lifetimes between μ - 3σ and μ + 3σ
100 - 99.7 = 0.3/2 = 0.15 %
According to the Empirical rule, 0.15% lightbulbs will last less than 441 hours.
