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For question 2.37 part a, Why are the mu and sigma parameters calculated like that?

For question 2.37 part a, Why are the mu and sigma parameters calculated like that?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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For question 2.37 part a, Why are the mu and sigma parameters calculated like that?

P(L > 10000) Following above procedure In T –u Z = In 10000-9.3790 = -1.0187 0.1655 P(Z) = 0.1538 P(L>10000) = 1 – P(L<10000) = 1 –- 0.1538 = 0.846 P(L=12000 | L>10000) = 0.468 * 1/ 0.846 = 0.55324
Transcribed Image Text:P(L > 10000) Following above procedure In T –u Z = In 10000-9.3790 = -1.0187 0.1655 P(Z) = 0.1538 P(L>10000) = 1 – P(L<10000) = 1 –- 0.1538 = 0.846 P(L=12000 | L>10000) = 0.468 * 1/ 0.846 = 0.55324
Prob 2.37 - The life of a light bulb is lognormally distributed with mean of 12,000 h and standard deviation of 2000 h. Compute the probability that a) A light bulb will last 12,000h b) A light that has already worked for 10,000 h will last 12,000 h ANS: Given Hy = 12000, oy = 2000 He= In = 9.379 1+0*o O *0 Of = In | =0.1655 Р(В> 12000) First we have find Z values for which from the tables we get P(B<12000). In T-H Z = In 12000-9.3790 = 0.0827 0.1655 P(Z=0.0827) = 0.532 P(B>12000) = 1 - P(B<12000) = 1 - 0.532 = 0.468 P(L=12000 | L>10000) P(L=12,000)× P (L>10,000V L=12,000) P(L>10000)
Transcribed Image Text:Prob 2.37 - The life of a light bulb is lognormally distributed with mean of 12,000 h and standard deviation of 2000 h. Compute the probability that a) A light bulb will last 12,000h b) A light that has already worked for 10,000 h will last 12,000 h ANS: Given Hy = 12000, oy = 2000 He= In = 9.379 1+0*o O *0 Of = In | =0.1655 Р(В> 12000) First we have find Z values for which from the tables we get P(B<12000). In T-H Z = In 12000-9.3790 = 0.0827 0.1655 P(Z=0.0827) = 0.532 P(B>12000) = 1 - P(B<12000) = 1 - 0.532 = 0.468 P(L=12000 | L>10000) P(L=12,000)× P (L>10,000V L=12,000) P(L>10000)
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