Question

Question content area top Part 1 Use the given values of n=2112 and p= 3 4 to find the maximum value that is significantly​ low, μ−2σ​, and the minimum value that is significantly​ high, μ+2σ. Round your answer to the nearest tenth unless otherwise noted.

Answer 1

To find the maximum value that is significantly low (μ - 2σ) and the minimum value that is significantly high (μ + 2σ), use the formulas and the given values of n = 2112 and p = 3/4. The maximum value that is significantly low is approximately 1544.202, and the minimum value that is significantly high is approximately 1623.798.

Step-by-step explanation:

To find the maximum value that is significantly low, you can use the formula μ - 2σ. Given the values of n = 2112 and p = 3/4, we need to calculate the mean (μ) and the standard deviation (σ) first. The mean (μ) is n * p = 2112 * (3/4) = 1584. The standard deviation (σ) is √(n * p * (1-p)) = √(2112 * (3/4) * (1-3/4)) = √(2112 * (3/4) * (1/4)) = √(2112 * 3/16) = √(6336/16) = √396 = 19.899. As a result, the maximum value that is significantly low, μ - 2σ, is 1584 - 2 * 19.899 = 1584 - 39.798 = 1544.202.

To find the minimum value that is significantly high, you can use the formula μ + 2σ. Using the same mean (μ) and standard deviation (σ) values, the minimum value that is significantly high, μ + 2σ, is 1584 + 2 * 19.899 = 1584 + 39.798 = 1623.798.