SOLUTION: 4. Answer the questions about the specified normal distribution. a.The lifetime of ZZZ batteries are normally distributed with a mean of 270 hours and a standard deviation &#

Algebra ->  Probability-and-statistics -> SOLUTION: 4. Answer the questions about the specified normal distribution. a.The lifetime of ZZZ batteries are normally distributed with a mean of 270 hours and a standard deviation &#      Log On


   

Question 322162: 4. Answer the questions about the specified normal distribution.

a.The lifetime of ZZZ batteries are normally distributed with a mean of 270 hours and a standard deviation  of 10 hours. Find the number of hours that represent the 40th percentile.

b.Scores on an English placement test are normally distributed with a mean of 55 and standard deviation  of 6.5. Find the score that marks the top 5%.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a.The lifetime of ZZZ batteries are normally distributed with a mean of 270 hours and a standard deviation  of 10 hours. Find the number of hours that represent the 40th percentile.
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Find the z-value that has a left tail of 40%
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z = invNorm(0.40) = -0.2533
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Find the corresponding x-value using x = zs+u:
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x = -0.2533*10 + 270
x = 267.46
Round up to x = 268
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b.Scores on an English placement test are normally distributed with a mean of 55 and standard deviation  of 6.5. Find the score that marks the top 5%.
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Find the z-value with a left tail of 95%.
invNorm(0.95) = 1.645
Find the corresponding x value:
x = 1.645*10+270 = 286.45
Round up to x = 287
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Cheers,
Stan H.
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