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 the40th percentile. (3 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 5%. (3 points)

Explanation / Answer

(a) Given X~Normal(=265, =10) The probability is P(X P((X-)/ < (c-265)/10)=0.4 --> (c-265)/10 = -0.253 (check normal table) --> c= 265 -10*0.253 = 262.47 (b) Given X~Normal(=36, =6.5) P(XP(Z (c-36)/6.5 = 1.645 (check normal table) --> c=36+6.5*1.645=46.6925

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