**Market Research Group Probability Study**A market research group assumes that $ p = 25\% $ of customers would be willing to upgrade their services. A sample of $ n = 300 $ customers would be polled, and the random variable $ Y $ indicates a count of positive responses.**Use Normal Approximation to the Binomial for the Following Questions:**1. **Evaluate the Probability that $ Y $ would be above 87.**2. **Find the Chance of Having 60 to 69 Positive Answers.**3. **Determine How Likely the Value of $ Y $ would Exceed 72.**4. **Evaluate Approximate Values $ y_{(0.05)} $ and $ y_{(0.95)} $ such that Only 5% would be Above $ y_{(0.05)} $ and Also 5% would be Below $ y_{(0.95)} $.** **Study Involving Sample Proportion Analysis**A study involves $ n = 225 $ students. Researchers expect that 10% of them would change their major within the next two semesters. **Use sampling distribution of the sample proportion to answer the questions below.**1. **Determine parameters** of approximating normal distribution for sample proportion of students who would change their major.2. What is the chance that a sample proportion of those students **would exceed 9%?**3. Determine approximate probability that the sample proportion **would be below 12.5%.**4. Evaluate the chance of having the sample proportion **between 9.5% and 11.5%.**

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Market research group assumes that p = A sample of n = 25% of customers would be willing to upgrade their services. 300 customers would be polled and random variable Y indicates a count of positive responses. Use Normal Approximation to the Binomial for next questions 1. Evaluate probability that Y would be above 87 2. Find the chance of having 60 to 69 positive answers 3. Determine how likely the value of Y would exceed 72 4. Evaluate approximate values y(0.05) and y(0.95) such that only 5% would be above 5% would be below y(0.95) Y(0.05) and also

Market research group assumes that p = A sample of n = 25% of customers would be willing to upgrade their services. 300 customers would be polled and random variable Y indicates a count of positive responses. Use Normal Approximation to the Binomial for next questions 1. Evaluate probability that Y would be above 87 2. Find the chance of having 60 to 69 positive answers 3. Determine how likely the value of Y would exceed 72 4. Evaluate approximate values y(0.05) and y(0.95) such that only 5% would be above 5% would be below y(0.95) Y(0.05) and also

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Market Research Group Probability Study**

A market research group assumes that $ p = 25\% $ of customers would be willing to upgrade their services. A sample of $ n = 300 $ customers would be polled, and the random variable $ Y $ indicates a count of positive responses.

**Use Normal Approximation to the Binomial for the Following Questions:**

1. **Evaluate the Probability that $ Y $ would be above 87.**

2. **Find the Chance of Having 60 to 69 Positive Answers.**

3. **Determine How Likely the Value of $ Y $ would Exceed 72.**

4. **Evaluate Approximate Values $ y_{(0.05)} $ and $ y_{(0.95)} $ such that Only 5% would be Above $ y_{(0.05)} $ and Also 5% would be Below $ y_{(0.95)} $.**

**Study Involving Sample Proportion Analysis**

A study involves $ n = 225 $ students. Researchers expect that 10% of them would change their major within the next two semesters.

**Use sampling distribution of the sample proportion to answer the questions below.**

1. **Determine parameters** of approximating normal distribution for sample proportion of students who would change their major.

2. What is the chance that a sample proportion of those students **would exceed 9%?**

3. Determine approximate probability that the sample proportion **would be below 12.5%.**

4. Evaluate the chance of having the sample proportion **between 9.5% and 11.5%.**

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