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 to the cement plant, fill up, and return to the construction site with another load of cement. From past experience, it is known that the mean cycle time is μ = 40 minutes with σ = 14 minutes. The x distribution is approximately normal.

(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.)

Answer 1

The random variable X denotes cycle time in minutes for the truck to leave the construction site.

Given : X ~ N(mu =40 , Sigma² = 14²)

Required Probability = P ( X> 55 / X >40 )

P(X >55) = P ( ( X-mu) /sigma > (55-40)/14)

= P ( Z > 1.0714) Since Z = ( X-mu) /sigma ~ N(0,1).

From normal probability table.

P(Z >1.0714) = 0.1420

P(X >40) = P ( ( X-mu) /sigma > (40-40)/14)

= P(Z >0)

From normal probability table

P(Z >0 ) = 0.5000

Hence P ( X >55 / X >40) = 0.1420 / 0.5000 = 0.2840

P ( The cycle time exceed 55 minutes given that it has exceeded 40 minutes.) =0.2840.