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ECN 422

PS 4

Due in class on Nov 7th

Part 1 Summary

Read textbook Chapters 4.1-4.3 and 5.1-5.4 and write a minimum two-page summary

Part 2 Questions

Normal Distribution

Question 1

Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 15.0 kips and standard deviation 1.25 kips. Compute the following probabilities by stan-dardizing and then using the normal distribution table, say Table A.3 in the textbook.

a) P(X ≤ 15) b) P(X ≤ 17.5)

c) P(X ≥ 10) d) P(14 ≤ X ≤ 18)

e) P(|X - 15| ≤ 3)

Question 2

In a road-paving process, asphalt mix is delivered to the hopper of the paver by trucks that haul the material from the batching plant. The article ìMod-eling of Simultaneously Continuous and Stochastic Construction Activities for Simulationî (J. of Construction Engr. and Mgmnt., 2013: 1037-1045) proposed a normal distribution with mean value 8.46 min and standard deviation .913 min for the rv X = truck haul time.

a) What is the probability that haul time will be at least 10 min? Will exceed 10 min?

b) What is the probability that haul time will exceed 15 min?

c) What is the probability that haul time will be between 8 and 10 min?

d) What value c is such that 98% of all haul times are in the interval from 8:46 - c to 8.46 + c?

e) If four haul times are independently selected, what is the probability that at least one of them exceeds 10 min?

Distribution of the Sum and Average

Question 3

A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. Twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the remaining 30% choose a 65-oz box. Let X1 and X2 denote the package sizes selected by two independently selected purchasers.

a) Determine the sampling distribution of X = (X1+X2)=2, calculate E(X), and compare to E (X1).

b) Determine the sampling distribution of the sample variance S 2 , calculate E(S2), and compare to V ar (X1).

Question 4

The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min?