Section 5.3: NormalDistributions: Finding Values 4. Answer the questions about t

Question

Section 5.3: NormalDistributions: Finding Values

4. Answer the questions about thespecified normal distribution. (References: example 4 and 5page 264 - 265, end of section exercises 39 – 45 pages267 - 268)

a.    The lifetime of ZZZ batteries are normallydistributed with a mean of 265 hours and a standard deviation s of10 hours. Find the number of hours that represent the the25th percentile. (2.5 points)

b.    Scores on an English placement test arenormally distributed with a mean of 36 and standard deviation s of6.5. Find the score that marks the top 10%. (2.5 points)

Explanation / Answer

The lifetime of ZZZ batteries are normallydistributed with a mean of 265 hours and a standard deviation of 10hours. Find the number of hours that represent the the 40thpercentile.

so On the zscore table i had to find something as close as 40.
So Z, 0.26= .3974 and Z, -0.25 = .4013. those are the closest to40.

so did i do this right, and if so which one is correct?

265+ =0.256(10)= 262.44

or

265 + - 0.255(10)= 267.55 Z = -0.25335
Then hours = 265 - 0.25335*10 = 262.4665 Z = -0.25335
Then hours = 265 - 0.25335*10 = 262.4665 Z = -0.25335
Then hours = 265 - 0.25335*10 = 262.4665

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