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A poll is given, showing 70% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 6 of them favor the new building project?

A poll is given, showing 70% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 6 of them favor the new building project?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Review for Test 2** - **Score:** 5/16 - **Questions Answered:** 5/16 - **Progress:** Saved - **Status:** Done --- **Question 11** A poll is given, showing 70% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 6 of them favor the new building project? (Insert your answer in the text box below) --- **Options:** - Submit Question - Jump to Answer --- This is a probability question related to polling results, often relevant in statistics or mathematics courses. It requires calculating the probability of a specific number of favorable responses out of a sample, given a known proportion of the population.
Transcribed Image Text:**Review for Test 2** - **Score:** 5/16 - **Questions Answered:** 5/16 - **Progress:** Saved - **Status:** Done --- **Question 11** A poll is given, showing 70% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 6 of them favor the new building project? (Insert your answer in the text box below) --- **Options:** - Submit Question - Jump to Answer --- This is a probability question related to polling results, often relevant in statistics or mathematics courses. It requires calculating the probability of a specific number of favorable responses out of a sample, given a known proportion of the population.
Title: Analyzing Viewership Data for "Green's Anatomy" ### Background The television show *Green's Anatomy* has enjoyed long-standing success. Recently, it achieved a viewership share of 17%. This statistic implies that 17% of the TV sets in use at the time are tuned to *Green's Anatomy*. To verify this figure, an advertiser conducts a survey involving 13 households with active TV sets during a *Green's Anatomy* broadcast. ### Probability Analysis 1. **Probability of No Households Tuned In** Calculate the probability that none of the 13 households are watching *Green's Anatomy*. - \( P(\text{none}) = \_\_\_\_ \) 2. **Probability of At Least One Household Tuned In** Determine the probability that at least one household is tuned to *Green's Anatomy*. - \( P(\text{at least one}) = \_\_\_\_ \) 3. **Probability of At Most One Household Tuned In** Find the probability that at most one household is tuned into the show. - \( P(\text{at most one}) = \_\_\_\_ \) ### Consideration Evaluate whether having at most one household tuned to *Green's Anatomy* suggests that the 17% share value is incorrect. Consider if this scenario (at most one tuned household) is unusual when assessing the validity of the 17% viewership claim.
Transcribed Image Text:Title: Analyzing Viewership Data for "Green's Anatomy" ### Background The television show *Green's Anatomy* has enjoyed long-standing success. Recently, it achieved a viewership share of 17%. This statistic implies that 17% of the TV sets in use at the time are tuned to *Green's Anatomy*. To verify this figure, an advertiser conducts a survey involving 13 households with active TV sets during a *Green's Anatomy* broadcast. ### Probability Analysis 1. **Probability of No Households Tuned In** Calculate the probability that none of the 13 households are watching *Green's Anatomy*. - \( P(\text{none}) = \_\_\_\_ \) 2. **Probability of At Least One Household Tuned In** Determine the probability that at least one household is tuned to *Green's Anatomy*. - \( P(\text{at least one}) = \_\_\_\_ \) 3. **Probability of At Most One Household Tuned In** Find the probability that at most one household is tuned into the show. - \( P(\text{at most one}) = \_\_\_\_ \) ### Consideration Evaluate whether having at most one household tuned to *Green's Anatomy* suggests that the 17% share value is incorrect. Consider if this scenario (at most one tuned household) is unusual when assessing the validity of the 17% viewership claim.
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