A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey found that 85% of parents of teenagers have taken their teenager's cell phone or Internet privileges away as a punishment. You randomly select 14 parents of teenagers and ask them whether they have taken their teenager's cell phone or Internet privileges away as a punishment. Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. O A. Yes, the mean is and the standard deviation is (Round to two decimal places as needed.) O B. No, because nq < 5. O C. No, because np < 5.

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Please answer the following 2 questions
**Educational Text: Understanding Binomial Distributions and Normal Approximation**

**Problem 5.5.18**

In this problem, we explore whether we can use the normal distribution to approximate a binomial distribution. To do this, we need to consider the mean and standard deviation of the data provided. Here’s the scenario:

A survey reveals that 85% of parents of teenagers have taken away their teenager's cell phone or Internet privileges as a punishment. You randomly select 14 parents of teenagers and ask them whether they have done this.

**Deciding on Normal Approximation:**

When deciding if you can approximate a binomial distribution with a normal distribution, you need to consider the conditions where `np` and `nq` (where q = 1-p) are both greater than 5. 

- **p** (the probability of success) = 0.85
- **n** (the number of trials) = 14

Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice:

- **A.** Yes, the mean is [Box] and the standard deviation is [Box]. (Round to two decimal places as needed.)

- **B.** No, because nq < 5.

- **C.** No, because np < 5.

**Solution Approach:**

To proceed, calculate:

1. **Mean (μ):** \( \mu = np \)
2. **Standard Deviation (σ):** \( \sigma = \sqrt{npq} \)

Use these formulas to solve and determine whether both np and nq are greater than 5 to validate normal approximation. If they are, calculate and fill in the mean and standard deviation for a valid approximation. If not, select the correct rationale depending on which condition is not satisfied.
Transcribed Image Text:**Educational Text: Understanding Binomial Distributions and Normal Approximation** **Problem 5.5.18** In this problem, we explore whether we can use the normal distribution to approximate a binomial distribution. To do this, we need to consider the mean and standard deviation of the data provided. Here’s the scenario: A survey reveals that 85% of parents of teenagers have taken away their teenager's cell phone or Internet privileges as a punishment. You randomly select 14 parents of teenagers and ask them whether they have done this. **Deciding on Normal Approximation:** When deciding if you can approximate a binomial distribution with a normal distribution, you need to consider the conditions where `np` and `nq` (where q = 1-p) are both greater than 5. - **p** (the probability of success) = 0.85 - **n** (the number of trials) = 14 Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice: - **A.** Yes, the mean is [Box] and the standard deviation is [Box]. (Round to two decimal places as needed.) - **B.** No, because nq < 5. - **C.** No, because np < 5. **Solution Approach:** To proceed, calculate: 1. **Mean (μ):** \( \mu = np \) 2. **Standard Deviation (σ):** \( \sigma = \sqrt{npq} \) Use these formulas to solve and determine whether both np and nq are greater than 5 to validate normal approximation. If they are, calculate and fill in the mean and standard deviation for a valid approximation. If not, select the correct rationale depending on which condition is not satisfied.
The text describes a survey conducted among adults aged 33 to 51 in Country A regarding sports participation. According to the survey, 70% of adults reported participating in at least one sport. When selecting a random sample of 350 people in this age group, it was found that 40% reported participating in at least one sport. The question posed is about the likelihood and representativeness of this sample.

Following the text, there are multiple-choice options asking readers to determine the likelihood of the survey results based on probability, specifically if it is greater or less than 0.05. The options are:

A. The result is highly unlikely because its probability is greater than 0.05. Thus, the sample is a good representative sample.

B. The result is highly likely because its probability is greater than 0.05. Thus, the sample is not a good representative sample.

C. The result is highly unlikely because its probability is less than 0.05. Thus, the sample is not a good representative sample.

D. The result is highly likely because its probability is less than 0.05. Thus, the sample is not a good representative sample.

Additionally, there is an image of a bar chart titled "How adults get physical,” showing the preference percentages for different sports:

- Swimming: 16%
- Bicycling, golf: 12%
- Hiking: 11%
- Softball, walking: 10%
- Fishing: 9%
- Tennis: 6%
- Bowling, running: 4%
- Aerobics: 2%

This data is useful for understanding the distribution of sports participation among the surveyed adults.
Transcribed Image Text:The text describes a survey conducted among adults aged 33 to 51 in Country A regarding sports participation. According to the survey, 70% of adults reported participating in at least one sport. When selecting a random sample of 350 people in this age group, it was found that 40% reported participating in at least one sport. The question posed is about the likelihood and representativeness of this sample. Following the text, there are multiple-choice options asking readers to determine the likelihood of the survey results based on probability, specifically if it is greater or less than 0.05. The options are: A. The result is highly unlikely because its probability is greater than 0.05. Thus, the sample is a good representative sample. B. The result is highly likely because its probability is greater than 0.05. Thus, the sample is not a good representative sample. C. The result is highly unlikely because its probability is less than 0.05. Thus, the sample is not a good representative sample. D. The result is highly likely because its probability is less than 0.05. Thus, the sample is not a good representative sample. Additionally, there is an image of a bar chart titled "How adults get physical,” showing the preference percentages for different sports: - Swimming: 16% - Bicycling, golf: 12% - Hiking: 11% - Softball, walking: 10% - Fishing: 9% - Tennis: 6% - Bowling, running: 4% - Aerobics: 2% This data is useful for understanding the distribution of sports participation among the surveyed adults.
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