Can someone assist me in answering this question.
Use the given values of n and p to find the mimimum usual value of u-2standard deviations and the maximum ususual values u+20. n-186, p=0.13
To find the minimum usual value of u-2 standard deviations and the maximum unusual value of u+20, we need to calculate the mean (u) and the standard deviation.
Step 1: Find the mean (u)
The mean (u) can be calculated using the formula u = n * p, where n is the sample size and p is the probability.
Given values:
n = 186
p = 0.13
Calculating the mean:
u = 186 * 0.13
u = 24.18
The mean (u) is approximately 24.18.
Step 2: Find the standard deviation
The standard deviation can be calculated using the formula σ = √(n * p * (1 - p)), where n is the sample size and p is the probability.
Calculating the standard deviation:
σ = √(186 * 0.13 * (1 - 0.13))
σ = √(186 * 0.13 * 0.87)
σ ≈ √(21.8736)
σ ≈ 4.677
The standard deviation (σ) is approximately 4.677.
Step 3: Calculate the minimum usual value of u-2 standard deviations
The minimum usual value of u-2 standard deviations can be calculated by subtracting 2 times the standard deviation from the mean (u).
Minimum usual value = u - 2σ
Calculating the minimum usual value:
Minimum usual value = 24.18 - 2 * 4.677
Minimum usual value ≈ 24.18 - 9.354
Minimum usual value ≈ 14.826
The minimum usual value of u-2 standard deviations is approximately 14.826.
Step 4: Calculate the maximum unusual value of u+20
The maximum unusual value of u+20 can be calculated by adding 20 to the mean (u).
Maximum unusual value = u + 20
Calculating the maximum unusual value:
Maximum unusual value = 24.18 + 20
Maximum unusual value = 44.18
The maximum unusual value of u+20 is exactly 44.18.
Therefore, the minimum usual value of u-2 standard deviations is approximately 14.826, and the maximum unusual value of u+20 is exactly 44.18.