Question
In Mexico, the average annual consumption of alcohol per individual is 4,400 ml; however, the consumption pattern is characterized by being excessive, since large quantities are consumed in short periods, mainly on weekends. Assuming that alcohol consumption follows a normal distribution and a standard deviation of 200 ml. a) Calculate the probability that a person consumes more than 4000 ml per year? b) If a sample of 50 people is selected, how many of them will consume more than 4000 ml per year?
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Answer to a math question In Mexico, the average annual consumption of alcohol per individual is 4,400 ml; however, the consumption pattern is characterized by being excessive, since large quantities are consumed in short periods, mainly on weekends. Assuming that alcohol consumption follows a normal distribution and a standard deviation of 200 ml. a) Calculate the probability that a person consumes more than 4000 ml per year? b) If a sample of 50 people is selected, how many of them will consume more than 4000 ml per year?
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4.999 Answers
1. Calculate the z-score for 4000 ml:
z = \frac{4000 - 4400}{200} = \frac{-400}{200} = -2
2. Find the probability corresponding to the z-score:
P(Z > -2) = 0.9772
Answer:
P(X > 4000) = 0.9772
b) If a sample of 50 people is selected, how many of them will consume more than 4000 ml per year?
[Solution]
48.86 \approx 49
[Step-by-Step]
1. From part (a), the probability that a single person consumes more than 4000 ml is:
P(X > 4000) = 0.9772
2. Calculate the expected number of people in a sample of 50:
\text{Expected number} = 0.9772 \times 50 = 48.86
Answer:
48.86 \approx 49
2. Find the probability corresponding to the z-score:
Answer:
b) If a sample of 50 people is selected, how many of them will consume more than 4000 ml per year?
[Solution]
[Step-by-Step]
1. From part (a), the probability that a single person consumes more than 4000 ml is:
2. Calculate the expected number of people in a sample of 50:
Answer:
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