Ap statistics Murder Mystery



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Murder Mystery

Lethal Weapon
After doing the calculations, discard the weapon with the lowest probability of success.
If the Power Shock was the murder weapon, it was most likely used to electrocute the victim. Suppose that it could possibly take up to five direct shocks with the Power Shock to kill a victim and that the probability of a successful direct shock on any given attempt is 0.8. Assume that the murderer can take up to 6 attempts.
A. Which probability distribution should you use?

B. What is the probability of success? Failure?

C. If the murderer attempted the Power Shock up to 6 times, calculate the probability of electrocuting the kill having at least 5 direct shocks attempts?

If the M&M candy was the murder weapon, it is likely that the suspect created several poison M&M’s to increase the odds that the victim would be poisoned. From the M&M’s that were found at the scene, the police calculated the odds in favor of choosing a poisoned M&M over a purely chocolate M&M were 4 to 1.
D. Use this information to calculate the probability of choosing a poisoned M&M.
If the launched flying Gummy Bear was the murder weapon, it is likely that the suspect used the rubber bands from the launched pad to strangle the victim. Suppose that strangulation requires a minimum of 5 rubber bands. The probability distribution shows the probabilities associated with a varying number of rubber bands.


X = # of rubber bands

2

3

4

5

6

7

P(X)

n

n

n

2n

3n

2n

E. Use what you know about probability distributions to solve for n.

F. Calculate the expected number of rubber bands.

G. Find the probability that the murderer used five or more rubber bands.


H. Can you eliminate a murder weapon? Which one?

I. Which murder weapons remain?

J. Which suspects still remain?

K. Which locations still remain?




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