**Title: Using Normal Distribution to Approximate Binomial Distribution****Introduction:**In statistical analysis, determining when the normal distribution can approximate the binomial distribution is critical for simplifying complex probability calculations.**Scenario:**A survey of adults found that 8% say their favorite sport is auto racing. You randomly select 500 adults and ask them to name their favorite sport. Here, we'll explore whether a normal distribution can approximate this binomial distribution and solve for a specific probability.**Step-by-Step Exploration:**1. **Determine Conditions for Normal Approximation:** - The normal distribution can approximate the binomial distribution if both \( np \) and \( nq \) are greater than or equal to 5. - Here, \( p = 0.08 \) and \( n = 500 \). - Calculate: - \( np = 500 \times 0.08 = 40 \) - \( nq = 500 \times (1 - 0.08) = 460 \) Since both \( np \ge 5 \) and \( nq \ge 5 \), the normal distribution can approximate this situation. **Answer:** - **A. Yes, because both \( np \ge 5 \) and \( nq \ge 5 \).**2. **Calculate Probability:** - **(a)** Find the probability that the number of people who say auto racing is their favorite sport is at most 47. - This scenario sets up for a calculation using the normal approximation method to find relevant probabilities. **Instructions:** - Round to four decimal places as needed for the final answer. - Enter the answer in the provided space and use the corresponding tool to check the answer.**Conclusion:**This exercise demonstrates locating and verifying normal approximation conditions and paves the way for applying this method in more advanced statistical contexts.

Continuity correction factor table: If P(X=n) use P(n – 0.5 < X < n + 0.5)If P(X > n)…

Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults found that 8% say their favorite sport is auto racing. You randomly select 500 adults and ask them to name their favorite sport. Complete parts (a) through (d). Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. A. Yes, because both np 25 and nq 2 5. OB. No, because nq <5. OC. No, because np <5. (a) Find the probability that the number of people who say auto racing is their favorite sport is at most 47. (Round to four decimal places as needed.)

Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults found that 8% say their favorite sport is auto racing. You randomly select 500 adults and ask them to name their favorite sport. Complete parts (a) through (d). Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. A. Yes, because both np 25 and nq 2 5. OB. No, because nq <5. OC. No, because np <5. (a) Find the probability that the number of people who say auto racing is their favorite sport is at most 47. (Round to four decimal places as needed.)

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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