BONUS QUESTION ADD 2 POINTS TO TOTAL. A survey revealed that 4 amount of popcorn

Question

BONUS QUESTION ADD 2 POINTS TO TOTAL. A survey revealed that 4 amount of popcorn during a movie. If the next 17 mov ie goers are asked if they will eat popcorn during the next movie they attend, what is the probability that either at least 8 or at most 4 will say they will eat next movie? YOU ARE REQUIRED TO DISPLAY YOUR ANSWER WITH 4 DECIMAL PLACES BC 2 A game is played using three 6-sided dice. You throw these dice one time and if the dice all sho the same number (triples), you win $ 40.00. For this game to be "fair", how much should a person play this game ?

Explanation / Answer

#1.
p = 0.4

we can solve this using normal approximation method,
mean = 0.4 * 17 = 6.8
sd = sqrt(17*0.4*0.6) = 2.0199

P(X >= 8)
= P(X > 7.5) -- (continuity correction)
= P(z > (7.5 - 6.8)/2.0199)
= P(z > 0.3466)
= 0.3645 (using standard normal table)

P(X <= 4)
= P(X < 3.5) -- (continuity correction)
= P(z < (3.5 - 6.8)/2.0199)
= P(z > -1.6337)
= 0.0512 (using standard normal table)

Hence required probability = 0.3645 + 0.0512 = 0.4157

#2.
Probability of getting triples, p = 6/216 = 1/36
Let y be the amount should be paid.
In order to be a fair game, expected probability E(X) should be zero.

E(X) = x*35/36 - 40*1/36
35x = 40
x = 40/35 = 1.1429

Hence amount to be paid $1.1429

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