Question

Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ. Round your answer to the nearest hundredth unless otherwise noted.
n = 1056, p = 0.80

Answer 1

To find the minimum and maximum usual values, we first find the mean (μ) and standard deviation (σ) of the given data.

Mean (μ) = n * p,
where n = 1056 (number of trials) and p = 0.80 (probability of success).

μ = 1056 * 0.80 = 844.8

Standard deviation (σ) is given by the formula: σ = √(n * p * (1 - p))

σ = √(1056 * 0.80 * (1 - 0.80))
σ = √(844.8 * 0.20)
σ = √(168.96)
σ ≈ 12.997

Now that we have the mean and standard deviation, we can find the minimum and maximum usual values:

Minimum usual value (μ - 2σ) = 844.8 - 2 * 12.997
Minimum usual value ≈ 844.8 - 25.994
Minimum usual value ≈ 818.81 (rounded to the nearest hundredth)

Maximum usual value (μ + 2σ) = 844.8 + 2 * 12.997
Maximum usual value ≈ 844.8 + 25.994
Maximum usual value ≈ 870.79 (rounded to the nearest hundredth)

So, the minimum usual value is around 818.81 and the maximum usual value is around 870.79.