Given Information:
number of trials = n = 1042
Probability of success = p = 0.80
Required Information:
Maximum usual value = μ + 2σ = ?
Minimum usual value = μ - 2σ = ?
Answer:
Maximum usual value = 859.51
Minimum usual value = 807.78
Explanation:
In a binomial distribution, the mean μ is given by
μ = np
μ = 1042*0.80
μ = 833.6
The standard deviation is given by
σ = √np(1 - p)
σ = √1042*0.80(1 - 0.80)
σ = √833.6(0.20)
σ = 12.91
The Maximum and Minimum usual values are
μ + 2σ = 833.6 + 2*12.91
μ + 2σ = 833.6 + 25.82
μ + 2σ = 859.51
μ - 2σ = 833.6 - 25.82
μ - 2σ = 807.78
Therefore, the minimum usual value is 807.78 and maximum usual value is 859.51