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 = 1042, p = 0.80

Answer 1

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