Question

x-barstd de We are going to combine a couple of activities that we performed on the HW. The hypothetical15.1977 1.16544 is as follows: Do not touch these cell values. An international company, InterCo, has contracted with a housing construction company that has been selected to construct a new tract of 193 upscale homes for several families that are being relocated to start a new InterCo facility. Families will be phased in at this new tract, so having a reasonable degree of confidence about when each house will be completed is very important. To this end, the construction company will pay penalties if the houses are either completed too early or too late. But select them for your calculations at the right - Data (in units of calendar weeks) from 213 previous similar construction jobs (houses) are found below this text box. Interco would like to have each house be completed in 15 1 weeks (i.e., 14-16 weeks). You are permitted to freeze cells along Row 3 If the company completes too soon ( -175.4% 2. What is the probability that a house will be completed more than 17 weeks from start? Answer -193.9% 3. What is the probability that a house will be completed in less than 14 weeks from start? Answer -15,2% 4. What is the probability that a house will be completed within the specified time frame of 14-16 weeks? Answer-> 309.196 5. Using your answer to #4, how many of the 193 houses are expected to be completed on time? Report to one decimal place. Answer houses 6. Using your answer to #3, what is the expected cost ($k) for completing too soon? Report to one decimal place. Answer 7, using your answers to #1 & #2, what is the expected cost ($k) for completing in 16-17 weeks? Report to one decimal place. Answer 8. Using your answer to #2, what is the expected cost ($k) for completing in more than 17 weeks? Report to one decimal place. Answer 9. Using the SUM macro and your answers for #6-8, what is the total penalty the construction company is expected to pay? Answer 10. What is the probability that a house will be completed in exactly 15 weeks? Answer

Answer 1

1.

P(X > 16) =P(Z > (16 - 15.1977)/1.16544) =P(Z > 0.6884) =0.246 =24.6%

2.

P(X > 17) =P(Z > (17 - 15.1977)/1.16544) =P(Z > 1.5465) =0.061 =6.1%

3.

P(X < 14) =P(Z < (14 - 15.1977)/1.16544) =P(Z < -1.0277) =0.152 =15.2%

4.

P(14 $\leq$ X $\leq$ 16) =P(-1.0277 $\leq$ Z $\leq$ 0.6884) =1 - 0.152 - 0.246 =0.602 =60.2%

5.

193*60.2% =116.2 houses are expected to be completed on time.

6.

The expected cost for completing too soon =10k*15.2% =1.5k

7.

P(16 < X $\leq$ 17) =P(X > 16) - P(X > 17) =0.246 - 0.061 =0.185 =18.5%.

So, the expected cost for completing in 16 - 17 weeks =15k*18.5% =2.8k

8.

The expected cost for completing in more than 17 weeks =20k*6.1% =1.2k

9.

The total penalty the construction company is expected to pay =1.5k + 2.8k + 1.2k =5.5k

10.

Since normal distribution is a continuous probability distribution, the probability that the normal random variable, X equals any exact value is always 0.

So, P(X =15) =0