Math 116 – 05: Extra Credit Opportunity 2
Name:
Each correct answer will be worth 1 point (no partial credit) added to your lowest test score. Put only final answers
on this sheet. Do all work on separate paper. All probabilities should be rounded to 4 decimal places (unless they
are exact). This is due (no exceptions) on Thursday, November 8, at the beginning of class.
1. A company bids for two contracts. Suppose the probability they get contract A is 0.8. If the
company gets contract A, the probability they also get contract B is 0.2, but if they do not get
contract A, the probability they get contract B is 0.4. The value of contract A is $10000,
while the value of contract B is $7500.
(a) If x is the money made by the company from these contracts, give the probability
model of x.
(b) What is the expected amount of money this company will make from these contracts?
(c) What is the standard deviation of the money made?
2. The Mars Candy Company claims that 10% of the M&M’s it produces are green. Suppose
that this is accurate. The candies are randomly packaged in small bags, each containing 30
M&M’s.
(a) What is the fewest number of bags of M&M’s that we must sample in order to claim
that the distribution of p̂ = the proportion of M&M’s in our sample that are green has
a normal distribution?
(b) If we sampled 10 such bags, what is the probability that the proportion of green
M&M’s in our sample is more than 12%?
(c) If we sampled 15 such bags, what is the probability that the proportion of green
M&M’s in our sample is less than 8.5%?
3. Farmers measure daily milk production in pounds. Ayrshire cows average 47 pounds of milk
per day with a standard deviation of 5 pounds. Assume that milk production by these cows
follows a normal model.
(a) What is the probability that one of these cows, randomly selected, produces more
than 55 pounds of milk in a day?
(b) What is the probability that if 64 of these cows are randomly selected, the average
amount of milk produced per day is more than 55 pounds?
(c) What is the probability that if 100 of these cows are randomly selected, the average
amount of milk produced per day is less than 45 pounds?
(d) What average amount of milk produced per day represents the highest 2% of all
averages for samples of size 100 for Ayrshire cows?
4. A city ballot includes a local initiative that would legalize gambling. The issue is hotly
contested, and the local newspaper decides to conduct a poll to predict the outcome. In a
random sample of 1200 people, 53% said they planned to vote “yes”.
(a) What would be the margin of error for a 90% confidence interval for the proportion
of all voters planning to vote “yes”?
(b) Construct a 97.6% confidence interval for the proportion of all voters planning to vote
“yes”?
(c) If we wanted to reduce the ME from part (a) by ½ without loosing any confidence,
how many voters would have to be polled?
5. A state’s environmental agency worries that many cars may be violating air emissions
standards. The agency hopes to check a sample of vehicles to estimate the percentage with a
margin of error of 3% and 90% confidence. To gauge the size of the problem, the agency
picks 60 cars and finds 9 with faulty emissions. How many cars must be sampled for a full
investigation (i.e. to construct the confidence interval described)?