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ere to view page 1 of the standard normal distribution table. ere to view page 2 of the standard normal distribution table. probability is to four decimal places as needed.) probability is

ere to view page 1 of the standard normal distribution table. ere to view page 2 of the standard normal distribution table. probability is to four decimal places as needed.) probability is

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Probability Analysis Based on Survey Data Researchers at a reputable university and a reputable health organization claim that approximately 75% of people believe "tranquilizers work very well to make a person more calm and relaxed." Of the next 85 people interviewed, the following probabilities are sought: - What is the probability that: (a) At least 55 out of 85 people are of this opinion? (b) At most 62 out of 85 people are of this opinion? To solve these questions, one can refer to the standard normal distribution tables. **Useful Links for Standard Normal Distribution Table:** - [Standard Normal Distribution Table - Page 1](#) - [Standard Normal Distribution Table - Page 2](#) --- #### Probability Calculations (a) The probability that at least 55 out of 85 people hold the opinion: \[ \text{The probability is } \boxed{ } \] (Round to four decimal places as needed.) (b) The probability that at most 62 out of 85 people hold the opinion: \[ \text{The probability is } \boxed{ } \] (Round to four decimal places as needed.) --- This approach uses the standard normal distribution to approximate the binomial probabilities given the large sample size. It requires converting the binomial distribution to a normal distribution using the mean and standard deviation formulae for a binomial variable. Then, the probabilities are found using the found Z-scores and the standard normal distribution table. *Note: The viewer is encouraged to use the provided links to the standard normal distribution tables for detailed step-by-step calculation.*
Transcribed Image Text:### Probability Analysis Based on Survey Data Researchers at a reputable university and a reputable health organization claim that approximately 75% of people believe "tranquilizers work very well to make a person more calm and relaxed." Of the next 85 people interviewed, the following probabilities are sought: - What is the probability that: (a) At least 55 out of 85 people are of this opinion? (b) At most 62 out of 85 people are of this opinion? To solve these questions, one can refer to the standard normal distribution tables. **Useful Links for Standard Normal Distribution Table:** - [Standard Normal Distribution Table - Page 1](#) - [Standard Normal Distribution Table - Page 2](#) --- #### Probability Calculations (a) The probability that at least 55 out of 85 people hold the opinion: \[ \text{The probability is } \boxed{ } \] (Round to four decimal places as needed.) (b) The probability that at most 62 out of 85 people hold the opinion: \[ \text{The probability is } \boxed{ } \] (Round to four decimal places as needed.) --- This approach uses the standard normal distribution to approximate the binomial probabilities given the large sample size. It requires converting the binomial distribution to a normal distribution using the mean and standard deviation formulae for a binomial variable. Then, the probabilities are found using the found Z-scores and the standard normal distribution table. *Note: The viewer is encouraged to use the provided links to the standard normal distribution tables for detailed step-by-step calculation.*
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