Assignment Guidelines:
o Your work must be organized neatly and typed.
o Clearly indicate your name and the assignment number in the file name.
o Electronic copies of your work can be submitted as an attachment to the drop box.
o You need to hand in individual work.
You may talk with each other about the problems.
However, everything in the assignment must be your own work.
o No late assignments will be accepted.
You do not need to do the calculations with a by hand, you can use Minitab Express to calculate the binomial probabilities.
Indicate the n and p for the Binomial setting and describe the steps taken to solve the problem.
1. Would the following examples qualify as binomial experiments? Explain your reasoning.
a. The number of people with blood type O-negative in a simple random sample of size 10 is recorded.
According to the Information Please Almanac, 6% of the human population is blood type O-negative.
b. A probability experiment in which three cards are drawn from a deck without replacement and the number of aces is recorded.
2. According to the American Red Cross, approximately 10% of the human population is blood type Bpositive.
If we select 20 people at random, find the probability that more than 3 people in the sample have blood type B-positive. Is this unusual?
3. The Federal Bureau of Investigation (FBI) trains sniffer dogs to find explosive material.
At the end of the training, Maggie, the FBI's prize dog, is let loose in a field with four unmarked parcels, one of
which contains the Semtex explosive.
An experiment is performed 10 times to see if Maggie correctly identifies the correct parcel.
Maggie correctly identifies the correct parcel 8 of the 10 times.
Is Maggie better than an untrained dog?
Assume that an untrained dog has a probability of 0.25 of successfully identifying a parcel containing explosives.
Find the probability of an untrained dog correctly identifying the parcel 8 of the 10 times.
Is it unusual for an untrained dog to do as well as Maggie?
4. It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked.
A grocery store purchases a random sample of 100 frozen chickens.
a. What is the probability that the store will have at least 20 contaminated chickens?
b. On average, how many contaminated chickens will be in the sample of 100 chickens?