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Researchers at a reputable university and a reputable health organization claim that approximately 74% 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 53 are of this opinion? (b) at most 61 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. (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.)

Researchers at a reputable university and a reputable health organization claim that approximately 74% 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 53 are of this opinion? (b) at most 61 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. (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.)

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 and Opinion Polls on Tranquilizers Researchers at a reputable university and a reputable health organization claim that approximately 74% 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 53 are of this opinion? (b) At most 61 are of this opinion? **Instructions:** - To calculate these probabilities, you may need to refer to the standard normal distribution tables. - Click the links below to access the necessary tables: - [Click here to view page 1 of the standard normal distribution table.](#) - [Click here to view page 2 of the standard normal distribution table.](#) **Calculations:** 1. **(a) The probability is:** ⬜ (Round to four decimal places as needed.) 2. **(b) The probability is:** ⬜ (Round to four decimal places as needed.) ### How to Interpret the Graphs and Diagrams The standard normal distribution table (Z-table) provides the area (or probability) to the left of a given Z-score in a standard normal distribution. You can use these tables to find the probability corresponding to a particular Z-score value. - **Page 1 of the standard normal distribution table** generally includes Z-scores ranging from negative infinity up to a Z-score of zero. - **Page 2 of the standard normal distribution table** typically covers Z-scores from zero to positive infinity. You will use these tables to find the cumulative probabilities, which will help you in determining the overall probabilities for events (a) and (b). **Example Calculation Steps:** 1. Calculate the mean (μ) and standard deviation (σ) for the given scenario. 2. Convert the specific count values (53 and 61) into Z-scores. 3. Use the Z-scores to find the corresponding probabilities from the standard normal distribution tables. 4. Round the results to four decimal places as requested.
Transcribed Image Text:### Probability and Opinion Polls on Tranquilizers Researchers at a reputable university and a reputable health organization claim that approximately 74% 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 53 are of this opinion? (b) At most 61 are of this opinion? **Instructions:** - To calculate these probabilities, you may need to refer to the standard normal distribution tables. - Click the links below to access the necessary tables: - [Click here to view page 1 of the standard normal distribution table.](#) - [Click here to view page 2 of the standard normal distribution table.](#) **Calculations:** 1. **(a) The probability is:** ⬜ (Round to four decimal places as needed.) 2. **(b) The probability is:** ⬜ (Round to four decimal places as needed.) ### How to Interpret the Graphs and Diagrams The standard normal distribution table (Z-table) provides the area (or probability) to the left of a given Z-score in a standard normal distribution. You can use these tables to find the probability corresponding to a particular Z-score value. - **Page 1 of the standard normal distribution table** generally includes Z-scores ranging from negative infinity up to a Z-score of zero. - **Page 2 of the standard normal distribution table** typically covers Z-scores from zero to positive infinity. You will use these tables to find the cumulative probabilities, which will help you in determining the overall probabilities for events (a) and (b). **Example Calculation Steps:** 1. Calculate the mean (μ) and standard deviation (σ) for the given scenario. 2. Convert the specific count values (53 and 61) into Z-scores. 3. Use the Z-scores to find the corresponding probabilities from the standard normal distribution tables. 4. Round the results to four decimal places as requested.
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