How to set up Probablity distribution? Is it necessary here

[Emily]

:shock: My final is in a week!\

Problem: An archer is in competition and must hit 8 bull's eyes out of 12 shots in order for the team to win. Based on previous experience the probability of the archer hitting the target is 0.550. (Assume the probability of hitting the target does not change after each shot).

a. What is the expected number of bull's eyes this archer will make?
b. What is the probability of the archer missing the target?
C. What is the probability that the archer will get exactly 8 bull's eyes.
I am assuming that I need to set up a probability distribution for this. To do so I have been using normalpdf on the calc and plugging in (12,.550, 1) (12,.550,2) (12,.550,3)..etc for the probability column. Is this correct?

 

[Guest]

Re: How to set up Probablity distribution? Is it necessary

:shock: My final is in a week!\

Problem: An archer is in competition and must hit 8 bull's eyes out of 12 shots in order for the team to win. Based on previous experience the probability of the archer hitting the target is 0.550. (Assume the probability of hitting the target does not change after each shot).

There seems to be some confusion in this question between hitting the bull's eye and hitting the target. They are not usually the same thing.

Lets assume throughout the question refers either to bull's eyes or the target.

a. What is the expected number of bull's eyes this archer will make?

Expected number is equal to the probability of success on a single trial times the number of trials, you are given enough information to just write this down.

b. What is the probability of the archer missing the target?
C. What is the probability that the archer will get exactly 8 bull's eyes.

The number of hits in this type of problem has a binomial distribution. In the binomial distribution the probability of exactly \(\displaystyle \Large n\) success in \(\displaystyle \Large N\) trials is:

\(\displaystyle \Large
P(n,N)={N \choose n} p^n \ (1-p)^{N-n}\),

for b. you want \(\displaystyle \Large P(0,8)\) and for c. you want \(\displaystyle \Large P(8,8)\).

Notes from the department of useless information:
A archery target (FITA target archery type) is divided into 5 coloured rings from the centre outwards these are Gold (yellow), Red, Blue, Black and White. Each of these is subdivided by a line into two sub-rings.

RonL