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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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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