Statistics help

Question

You do not need to type in the formulas. Indicate the n and p for the Binomial setting and describe the steps taken to solve the problem

 

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 performing as well as Maggie. Is it unusual for an untrained dog to do as well as Maggie?

 

N=4 P=.5.  I am having a hard time with this problem and any help will be appreciated. It is due tomorrow and all week I have been struggling with this.

Answer 1

Anthony,

 

How about a couple of questions/hints to see if it gets you pointed in the right direction:

 

- For the untrained dog to do as well as Maggie did, what would the untrained dog have to be able to do, and how often would it have to be able to do it?  Just put that in English for a sec.

 

Let's change the experiment a little bit.  Instead of Maggie sniffing 4 packages, let's say she sniffs 5.  But everything else about the problem stays the same.  She still successfully sniffs the explosive 8 out of 10 times.  And let's assume that the same untrained dog still has a 25% chance of succeeding each time she tries to sniff the explosive. 

 

- Now, answer the same question.  In this new situation, what would the untrained dog have to be able to do, and how often would it have to be able to do it? 

 

In order to get things into "Binomial Speak," we need to translate that question into the quantities we need to know to calculate a binomial term.  Like, N and p.

 

- What does N represent?

- What does p represent?

 

If you look at your answers to the questions I asked above, and if you have an idea of what N and p mean, then that miiiight help you see what in this convoluted problem is related to N, and what is related to p...and which of the numbers in the problem have nothing to do with anything. 

 

Does that help at all?

 

-- Michael