FOLLOW ALL INSTRUCTIONS!!!!!!!!!!!!! !I\'d like you to complete the following pr
ID: 3312305 • Letter: F
Question
FOLLOW ALL INSTRUCTIONS!!!!!!!!!!!!!!I'd like you to complete the following problems on Excel. Copy the results to a Word document to be submitted and to uploaded through this assignment. Please also attach your Excel file where you entered the formulas.For each problem, I'd also like you to briefly describe the results in narrative form.
I NEED THE EXCEL SHEETS SHOWN FOR ANSWERS AS WELL AS EXPPLANATIONS!!!!!!!!!
(USE BINOMIAL) In the game of blackjack as played in casinos in Las Vegas, Atlantic City, Niagara Falls, as well as many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 45%. Find the probability that an average player wins. a Twice in 5 hands. b Ten or more times in 25 hands.
Explanation / Answer
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 5 * 0.45
= 2.25
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 5 * 0.45 * 0.55
= 1.2375
III.
standard deviation = sqrt( variance ) = sqrt(1.2375)
=1.1124
a.
the probability that an average player wins,twice in 5 hands
P( X = 2 ) = ( 5 2 ) * ( 0.45^2) * ( 1 - 0.45 )^3
= 0.3369
b.
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 25 * 0.45
= 11.25
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 25 * 0.45 * 0.55
= 6.1875
III.
standard deviation = sqrt( variance ) = sqrt(6.1875)
=2.4875
the probability that an average player wins ,Ten or more times in 25 hands
P( X < 10) = P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) +
= ( 25 9 ) * 0.45^9 * ( 1- 0.45 ) ^16 + ( 25 8 ) * 0.45^8 * ( 1- 0.45 ) ^17 + ( 25 7 ) * 0.45^7 * ( 1- 0.45 ) ^18 + ( 25 6 ) * 0.45^6 * ( 1- 0.45 ) ^19 + ( 25 5 ) * 0.45^5 * ( 1- 0.45 ) ^20 + ( 25 4 ) * 0.45^4 * ( 1- 0.45 ) ^21 + ( 25 3 ) * 0.45^3 * ( 1- 0.45 ) ^22 + ( 25 2 ) * 0.45^2 * ( 1- 0.45 ) ^23 + ( 25 1 ) * 0.45^1 * ( 1- 0.45 ) ^24 + ( 25 0 ) * 0.45^0 * ( 1- 0.45 ) ^25 +
= 0.2424
P( X > = 10 ) = 1 - P( X < 10) = 0.7576
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