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firasm committed Aug 13, 2023
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---
title: Underage drinking, Part II
topic: Distributions of random variables
author: Larry Gu
source: original
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params_vars_title: Underage drinking, Part II
params_n: 60
params_k: 54
params_mu: 42.0
params_sig: 3.55
params_Z: 3.38
params_Z4: 3.24
params_p4: 0.0006
---
# {{ params_vars_title }}
About $70$% of 18-20 year olds consumed alcoholic beverages in any given year. We now consider a random sample of ${{params_n}}$ 18-20 year olds.

## Part 1

How many people would you expect to have consumed alcoholic beverages?

## Part 2

And with what standard deviation? Round to 2 decimal places.

## Part 3

Would you be surprised if there were ${{params_k}}$ or more people who have consumed alcoholic beverages? Explain with Z-score.

## Part 4

What is the probability that ${{params_k}}$ or more people in this sample have consumed alcoholic beverages?
Use normal approximation and 0.5 correction. Round to 4 decimal places.

## Attribution

Problem is from the [OpenIntro Statistics](https://openintro.org/book/os/) textbook, licensed under the [CC-BY 4.0 license](https://creativecommons.org/licenses/by/4.0/).<br>![Image representing the Creative Commons 4.0 BY license.](https://raw.githubusercontent.com/firasm/bits/master/by.png)

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