σ = sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.8 * 0.2) / 100] = sqrt(0.0016) = 0.04
z = (p - P) / σ = (.73 - .80)/0.04 = -1.75. What type of formula is this problem?
Statistical?
express the square root of 0.0016 in standard form
The given formula is a standard deviation formula that is commonly used in statistics. This formula calculates the standard deviation (σ) of a sample proportion (P) based on the sample size (n) and the probability of success (P).
To calculate the standard deviation (σ), you need to multiply the probability of success (P) by the probability of failure (1 - P), and then divide the result by the sample size (n). The square root of this value gives you the standard deviation.
In this specific problem, the probability of success (P) is 0.8, the probability of failure is 1 - P = 0.2, and the sample size (n) is 100. Substituting these values into the formula gives:
σ = sqrt[ (0.8 * 0.2) / 100 ] = sqrt(0.0016) = 0.04
After calculating the standard deviation, you can then proceed to calculate the z-score. The z-score is a measure of how many standard deviations a given data point (p) is away from the mean (P). The formula for calculating the z-score is:
z = (p - P) / σ
In this problem, the value of p is 0.73, the mean (P) is 0.80, and the standard deviation (σ) is 0.04. Substituting these values into the formula gives:
z = (0.73 - 0.80) / 0.04 = -1.75
So, overall, this problem involves calculating the standard deviation of a sample proportion and then using that standard deviation to calculate the z-score.