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?

Miles
4.9
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

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

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