I need help soon as possible ### Determining the Sample SizeThe average cost of a gallon of unleaded gasoline in Greater Cincinnati was reported to be $2.41. During periods of rapidly changing prices, the newspaper samples service stations and prepares reports on gasoline prices frequently. Assume the standard deviation is $0.15 for the price of a gallon of unleaded regular gasoline, and recommend the appropriate sample size for the newspaper to use if the desired margin of error is $0.07.#### Explanation with Steps:1. **Identify the key parameters:** - Average cost (mean, μ): $2.41 - Standard deviation (σ): $0.15 - Desired margin of error (E): $0.07 - Confidence level: Typically 95% (which corresponds to a Z-score of approximately 1.96 for a normal distribution)2. **Use the formula for sample size calculation:** - $ n = \left( \frac{{Z \cdot \sigma}}{{E}} \right)^2 $ - Where: - $ n $ is the sample size - $ Z $ is the Z-score corresponding to the desired confidence level - $ \sigma $ is the standard deviation - $ E $ is the margin of error3. **Calculate the sample size:** - Plugging in the values: - $ n = \left( \frac{{1.96 \times 0.15}}{{0.07}} \right)^2 $ - First, calculate the numerator $ 1.96 \times 0.15 $: - $ 1.96 \times 0.15 = 0.294 $ - Next, divide by the margin of error $ 0.294 / 0.07 $: - $ 0.294 / 0.07 = 4.2 $ - Finally, square this value: - $ 4.2^2 = 17.64 $4. **Result:** - The sample size needed for the newspaper to achieve a margin of error of $0.07 with a 95% confidence level is approximately 18 (since the sample size must be a whole number, rounding up is appropriate).By following these calculations, it can be determined that the newspaper should sample approximately 18 service stations to report on gasoline prices with the

3. Determining the Sample Size: The average cost of a gallon of unleaded gasoline in Greater Cincinnati was reported to be $2.41. During periods of rapidly changing prices, the newspaper samples service stations and prepares reports on gasoline prices frequently. Assume the standard deviation is $0.15 for the price of a gallon of unleaded regular gasoline, and recommend the appropriate sample size for the newspaper to use if the desired margin of error is $0.07.

3. Determining the Sample Size: The average cost of a gallon of unleaded gasoline in Greater Cincinnati was reported to be $2.41. During periods of rapidly changing prices, the newspaper samples service stations and prepares reports on gasoline prices frequently. Assume the standard deviation is $0.15 for the price of a gallon of unleaded regular gasoline, and recommend the appropriate sample size for the newspaper to use if the desired margin of error is $0.07.

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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