Question 1063310: The lifespan in hours of a mass produced light optical device is normally distributed and has a mean of 1500 with a standard deviation of 350. What is the probability of one taken at random having a lifespan between 1500 and 1850 hours. If the guarantee is for 1000 hours, what percentage will fail to meet the guarantee?
What lifespan should be guaranteed if 95% must obtained?
Tks for your answer!!!!!!!!!!!!!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The lifespan in hours of a mass produced light optical device is normally distributed and has a mean of 1500 with a standard deviation of 350.
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a) What is the probability of one taken at random having a lifespan between 1500 and 1850 hours.
z(1500) = (1500-1500)/350 = 0
z(1850) = (1850-1500)/350 = 1
P(1500< x < 1850) = P(0< z < 1) = normalcdf(0,1) = 0.3413
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b) If the guarantee is for 1000 hours, what percentage will fail to meet the guarantee?
z(1000) = (1000-1500)/350 = -1.4286
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P(x < 1000) = P(z < -1.4286) = normalcdf(-100,-1.4286) = 0.0766
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c) What lifespan should be guaranteed if 95% must obtained ?
Draw a normal curve.
The upper 95% are the lifespans that meet the criteria.
The lower 5% do not.
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Find the z-value with a left tail of 5%::
invNorm(0.05) = -1.645
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Find the corresponding hour value using x = z*s + u
Ans:: x = -1.645*350 + 1500 = 925 hours
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Cheers,
Stan H.
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