Hello everyone. I need your help. I am struggling in answering this problem. So I'm hoping you could check my answers if they are correct. Thank you.
A team was formed to investigate the proliferation of counterfeit coins. It was found that the weight of genuine coins is normally distributed with µ = 27 grams and standard deviation = 4 grams, and the weight of counterfeit coins is normally distributed with µ = 23 grams and standard deviation= 5 grams. It was also estimated that 80% of coins in circulation are genuine, and the rest are counterfeit.
A. What is the probability that a cashier gives you a counterfeit coin that weighs more than 25 grams?
P(G) = 0.80 genuine coins in the circulation
P(C) = 0.20 counterfeit coins in the circulation
P(C ≥ 25) = (25-23)÷5 = 2/5 or 0.40
= 1 – P(z ≤ 0.4) = 1 – 0.6554
= 0.3446
P(C ≥ 25) = (0.3446) x (0.20) = 0.0689 or 6.89% - probability that a cashier gives you a counterfeit coin that weighs more than 25 grams.
B. What is the probability that a randomly chosen genuine coin weighs more than 25 grams?
P(G ≥ 25) = (25-27)÷4 = - 2/4 or -0.50
= P(z ≤ 0.50) = 0.6915
P(G ≥ 25) = (0.6915) x (0.80) = 0.5532 or 55.32% - probability that a randomly chosen genuine coin weighs more than 25 grams.
C. What is the probability that the cashier will give you a coin that weighs more than 25 grams and is a counterfeit?
P(≥25 Ω C) = P(G ≥ 25) x P(C ≥ 25)
= 0.5532 x 0.0689
= 0.0381 or 3.81% - probability that a cashier will give you a coin that weighs more than 25 grams and is a counterfeit
D. What is the probability that the coin from the cashier that weighs more than 25 grams is counterfeit?
P(≥25|C) = P(≥25 Ω C)P(C)
= 0.03810.20 = 0.1905 or 19.05% - probability that the coin from the cashier that weighs more than 25 grams is counterfeit.
Thanks again.
A team was formed to investigate the proliferation of counterfeit coins. It was found that the weight of genuine coins is normally distributed with µ = 27 grams and standard deviation = 4 grams, and the weight of counterfeit coins is normally distributed with µ = 23 grams and standard deviation= 5 grams. It was also estimated that 80% of coins in circulation are genuine, and the rest are counterfeit.
A. What is the probability that a cashier gives you a counterfeit coin that weighs more than 25 grams?
P(G) = 0.80 genuine coins in the circulation
P(C) = 0.20 counterfeit coins in the circulation
P(C ≥ 25) = (25-23)÷5 = 2/5 or 0.40
= 1 – P(z ≤ 0.4) = 1 – 0.6554
= 0.3446
P(C ≥ 25) = (0.3446) x (0.20) = 0.0689 or 6.89% - probability that a cashier gives you a counterfeit coin that weighs more than 25 grams.
B. What is the probability that a randomly chosen genuine coin weighs more than 25 grams?
P(G ≥ 25) = (25-27)÷4 = - 2/4 or -0.50
= P(z ≤ 0.50) = 0.6915
P(G ≥ 25) = (0.6915) x (0.80) = 0.5532 or 55.32% - probability that a randomly chosen genuine coin weighs more than 25 grams.
C. What is the probability that the cashier will give you a coin that weighs more than 25 grams and is a counterfeit?
P(≥25 Ω C) = P(G ≥ 25) x P(C ≥ 25)
= 0.5532 x 0.0689
= 0.0381 or 3.81% - probability that a cashier will give you a coin that weighs more than 25 grams and is a counterfeit
D. What is the probability that the coin from the cashier that weighs more than 25 grams is counterfeit?
P(≥25|C) = P(≥25 Ω C)P(C)
= 0.03810.20 = 0.1905 or 19.05% - probability that the coin from the cashier that weighs more than 25 grams is counterfeit.
Thanks again.
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