A cement truck delivers mixed cement to a large construction site. Let x represe

Question

A cement truck delivers mixed cement to a large construction site. Let x represent the cycle time in minutes for the truck to leave the construction site, go back experience, it is known that the mean cycle time is mu = 42 minutes with sigma = 19 minutes. The x distribution is approximately normal. (a) What is the probability that the cycle time will exceed 60 minutes, given that it has exceeded 50 minutes? (Round your answer to four decimal places.) (b) What is the probability that the cycle time will exceed 55 minutes, given that it has exceeded 40 minutes? (Round your answer to four decimal places.)

Explanation / Answer

Sample mean = 42 minutes and   = 19 minutes

so here we have to calculate probability that the cycle time will exceed 60 minutes , if it has already exceed 50 minutes.

so P( t > 60 / t> 50)

so we will calculate z - value for t = 50 and t = 60 seconds

so Z for t = 60 = > Z = (60 -42)/19 = 0.9473 so P(t> 60) = 1 - 0.828 = 0.172

and Z for t = 50 => Z = ( 50 - 42)/19 = 0.421 so P( t> 50) = 1 - 0.663 = 0.337

so P( t > 60 / t> 50) = 0.172/ 0.337 = 0.51

(b)

so here we have to calculate probability that the cycle time will exceed 60 minutes , if it has already exceed 50 minutes.

so P( t > 55 / t> 40)

so we will calculate z - value for t = 40 and t = 55 seconds

so Z for t = 55 = > Z = (55 -42)/19 = 0.6842 so P(t> 55) = 1 - 0.753 = 0.247

and Z for t = 40 => Z = ( 40 - 42)/19 = -0.1053 so P( t> 40) = 1 - 0.468 = 0.532

so P( t > 60 / t> 50) = 0.247/ 0.532 = 0.464

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