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, what is the probability that (a) at least 59 are of this opinion? (b) at most 64 are of this opinion? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.
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, what is the probability that (a) at least 59 are of this opinion? (b) at most 64 are of this opinion? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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For statistics
- [Click here to view page 2 of the standard normal distribution table.](https://www.example.com/page2_standard_normal_distribution)
#### Problem (a)
The probability that at least 59 out of 85 people believe that tranquilizers work to make a person more calm and relaxed. Provide the solution in the text box below.
`(a) The probability is [ ]`
*(Round to four decimal places as needed.)*
---
#### Problem (b)
The probability that at most 64 out of 85 people are of this opinion can be explored using the same method of normal approximation to the binomial distribution and the associated z-scores from the normal distribution table.
These structured steps guide students in understanding the relationship between empirical data and theoretical probability utilizing standard normal distribution tools.
---
By practicing these calculations, students can gain a firm grasp of statistical concepts applied to real-world studies and data interpretations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7a11c6-35df-4daf-855c-043e8f69fb75%2Fd2407aea-f34f-453a-81b4-7d6be413ce60%2Fm6ppols_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Analysis of Public Opinion on Tranquilizers
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." Given this claim, the probability questions are:
1. **For a sample of the next 85 people interviewed:**
- **What is the probability** that at least 59 people share this opinion?
- **What is the probability** that at most 64 people share this opinion?
To solve these problems, you will require access to the standard normal distribution table, often presented in multiple pages:
- [Click here to view page 1 of the standard normal distribution table.](https://www.example.com/page1_standard_normal_distribution)
- [Click here to view page 2 of the standard normal distribution table.](https://www.example.com/page2_standard_normal_distribution)
#### Problem (a)
The probability that at least 59 out of 85 people believe that tranquilizers work to make a person more calm and relaxed. Provide the solution in the text box below.
`(a) The probability is [ ]`
*(Round to four decimal places as needed.)*
---
#### Problem (b)
The probability that at most 64 out of 85 people are of this opinion can be explored using the same method of normal approximation to the binomial distribution and the associated z-scores from the normal distribution table.
These structured steps guide students in understanding the relationship between empirical data and theoretical probability utilizing standard normal distribution tools.
---
By practicing these calculations, students can gain a firm grasp of statistical concepts applied to real-world studies and data interpretations.
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