Select at least two of the following scenarios and answer the following for each

Question

Select at least two of the following scenarios and answer the following for each scenario you have chosen:

Does this scenario qualify as binomial?

If so, specify what a "P event" would be, and give the values of N, P, and Q (when possible).

If not, explain WHY it cannot be called binomial (that is, tell which condition or conditions for the binomial are not satisfied).

A. A kindergarten class has 25 children - 14 boys and 11 girls. The teacher wants to select 3 children for a play. She puts all the names into a hat and randomly chooses 3 names. We are interested in knowing how many boys are chosen.

B. You toss a fair coin 40 times and record the number of times you get tails.

C. You are visiting a foreign country where 25% of the population knows how to speak English. As you are exploring a city, you find yourself lost and in need of asking directions from the 8 people who are waiting at a bus stop. What are the chances that at least one of the people at the bus stop will be able to understand you and speak to you in English? (don't find the probability - just address the bullet points given above!)

D.   A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability that he hits the target more than twice? (just address the bullet points above)

E. Telephone surveying a group of 200 people to ask if they voted in the most recent local election (note we cannot know the value of P or Q without more information, but that does not necessarily mean that this is - or is not - a binomial scenario).

F. You take a survey of 50 traffic lights in a certain city, at 3 pm, recording whether the light was red, green, or yellow at that time.

G. You are at a fair, playing "pop the balloon" with 6 darts. There are 20 balloons. Ten of the balloons have a ticket inside that say "win," and 10 have a ticket that says "lose."

Explanation / Answer

A - Its binomial

N = 25

P = 14/25

Q = 11/25

B) In this problem since the success is not defined and the no of tails can have any value from 1 to 40, we cant consider the counting of no of tails as a binomial distribution.

C) It is binomial

P = 1/4

Q= 3/4

N = 8

D) Binomial

P= 4/5

Q = 1/5

N = 4

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