11/15/96 - 1001, 2001

Grammar Errors		Structure Errors
0	0.59	0	0.40
1	0.15	1	0.22
2	0.11	2	0.17
3	0.09	3	0.14
4	0.06	4	0.07

Use your calculators. Indicate what you input to ZCDF (or whatever program you use). The mean of the binomial is Np and the standard deviation is sqrt(n*p*(1-p))

1. English papers may contain two types of errors, grammatical and sentence structure. The table above gives the probability that a paper will contain the given number of errors of each type. Assume the two types are independent.
   1. Find the probability that a paper will contain a total of 6 errors.
   2. Find the mean number of grammar errors.
   3. Find the standard deviation of grammar errors.
   4. If I grade 60 papers, what is the most total grammar errors I will see (with probability 90%)?
2. The weight of sailors has a normal distribution with mean 160 lbs and standard deviation 20 lbs.
   1. What fraction of sailors weighs over 175 lbs?
   2. Find the weight, X, so that 90% of all sailors weigh more than X?
   3. I am going to carry 5 sailors in a small boat. The boat's capacity is 850 lbs. What is the chance we will not exceed its capacity?
3. Suppose that 20% of diners request French dressing.
   1. I have 50 servings of French dressing on hand. If there are 200 diners one night, what is the chance this will be enough?
   2. I expect 1,000 diners this week and am going to order French dressing. How many servings should I order to be 90% sure of having enough?
4. The county landfill receives both garbage trucks and dump trucks with rubble. The weights of each have a normal distribution. The weight of a garbage truck has a mean of 10 tons and a standard deviation of 0.8 tons. The weight of dump trucks has a mean of 7 tons and a standard deviation of 1.3 tons.
   1. What is the most a garbage truck will weigh (with probability 90%)?
   2. If 12 garbage trucks come in one day, what is the most they will haul (with probability 90%)?
   3. If 12 garbage trucks and 6 dump trucks all come in one day, what is the most they will haul altogether (with probability 90%)?
5. Suppose I am running the fish pond at a children's fair. Each child has a 25% of winning a prize. I brought 50 prizes.
   1. What is the chance I will be able to entertain 225 children without running out of prizes?
   2. How many children will I be able to serve (with probability 95%)?