SM230 - Test 2

17 Mar 97 - #1003, 2004, 3003 (Circle one)

You are encouraged to use calculators. Tell what program you used and the inputs to the program. Show probabilities to 4 decimal places. Circle your answers.

We are excavating an archaeological site concerning St. Patrick.

  1. About 4.5 noteworthy finds are made each day.
    1. We store these up at the site and take them to the lab each night. We have room for 6 finds. How often will this be enough room for a day's finds? [Ans: PCDF(L=4.5,T=1,X=6) = 0.83105]
    1. On Monday nights, there is no truck to the lab. How much space should we allocate to be 90% sure we can hold Monday's and Tuesday's finds? [Ans: 13 spaces. PCDF(L=4.5,T=2,X=13)=0.92615]
    2. Suppose we have room for 4 finds. When that space fills up, we'll call for the truck. It has been 0.8 days since we last called. What is the probability that the truck driver will not be needed in the next 0.4 days? [Ans: 0.41398 = 0.2133/0.5152 = PCDF(L=4.5,T=1.2,X=3)/PCDF(L=4.5,T=0.8,X=3)]
    3. I hate to miss a good find. How long (in 0.01 of a day) can I be gone from the site and have only a 50% chance of missing the next find? [Ans: 0.15 day]
  2. The site we are excavating was known to have 12 statues. 5 were of kings and 7 of saints. We have found 4 statues. What is the probability that we have at least one of each type of statue? [Ans: 0.91919 = HCDF(G=5,B=7,S=4,X=3)-HCDF(G=5,B=7,S=4,X=0)]
  3. Experience tells us that only about 15% of buckets of dirt have anything interesting in them.
    1. The crew has dug up 6 buckets. I'm tired and want to just dump them. What is the chance that there is anything interesting in this load? [Ans: 0.62285 = 1-BCDF(p=0.15,N=6,X=0)]
    2. I've searched through 10 buckets and haven't found any of them to be interesting. How unusual is this? [Ans: 0.19687 = BCDF(p=0.15,N=10,X=0)]
    3. If 10 buckets is a typical day, what is the greatest number (with probability 90%) of interesting buckets I will get? [Ans: 3. BCDF(p=0.15,N=10,X=3)=0.95]
    4. My sponsor is going to visit the site. I want to show him our progress. How many buckets should I be prepared to sift through to be 90% sure of finding something? [Ans: 15 or 14. BCDF(15)=0.087, BCDF(14)=0.10277]
  4. We want to show off our finds so far to our sponsor. We have 15 really old pieces and 12 just old pieces in storage.
    1. If we tell our lacky to bring us 6 pieces, what is the chance we will have at least 4 really old pieces? [Ans: 0.443 = 1-HCDF(G=15,B=12,S=6,X=3)]
    2. How many pieces should we request to have a 80% chance of at least 4 really old pieces? [Ans: 9. HCDF(S=9)=0.1090]
  5. A really good find comes about every 4.5 days.
    1. What is the probability of a good find in a week (7 days)? [Abs: 0.78893 = 1-PCDF(L=1/4.5,T=7,X=0)]
    2. What is the probability of no more than 1 week in 4 with a good find? [Ans: 0.03166 = BCDF(p=0.78893,N=4,X=1)]