Question

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There are two ways for a concrete truck to go from a ready-mixed concrete plant to the construction site. The first way is direct, for which the mean and standard deviation of travel time are 30 min and 5 min, respectively. The second way is through Town A. The mean and standard deviation of travel time between the plant and Town A are 14 min and 5 min, respectively. The mean and standard deviation of travel time between Town A and the construction site are 14 min and 6 min, respectively. If the total travel time is above 45 min, the concrete in the truck will go bad. Calculate the probability that the concrete goes bad for both cases of choosing the direct and indirect ways. Assume travel time has a normal distribution

Answer 1

Let Xa denote time required to go through direct way toorn plant to location. It is distributed a wemal with mean 30 min & standard deviation 5 min. let Xa denote time required to travel from plant to town A & from A to location. This is also normally distributed. It mean is sum of means of travel time from plant to I A4 A to location. So, it is 1444 = 28. minutes. The standard deviation of total route is √ (5)2 +62 - 25+36- rol = 7.8102 Regult used is XWEN (462) , & uncles 82) - Xitx, NNC with sto? Probability that form direct soute, time to commute is more than 45 minuts I P(Xd ) 45) - PlXd-304-30).

- P( 233) - HP(24) - 1-0.4987 - 0.043(0.0013) Probablity from and route through town A that commente time is more than 45 minutes is PL XAS45) - Plan -30 S 45-30) 7.8102 7.8102 - P(271.9206) 1-Plzc 1.9206) - 1-0.9726 = 0.0274 Here 2 is standard normal variate This obtained by subto acting a normal vasiate by mean and dividing by standard deviation. The cumalative distribution function of normal variate is obtained by using excel function HORMIDIST (2)

For example, p(x less than Or equal to 3) is.9987