Final answer:
To calculate the mean and standard deviation for the sum of samples when randomly selecting groups of checks which we get 7600 and 116.4, you apply the Central Limit Theorem, which involves multiplying the population mean by the sample size for the mean, and the population standard deviation by the square root of the sample size for the standard deviation.
Step-by-step explanation:
Finding the Mean and Standard Deviation in Sampling Distributions
To find the mean of the number of checks with a leading digit of 1 when groups of 784 checks are randomly selected, you would use Benford's law. However, the question does not provide the necessary specifics to apply Benford's law, so I will focus on the provided information regarding the Central Limit Theorem (CLT) to demonstrate how to compute the mean and standard deviation for a sum of samples.
Based on the information provided:
- The population mean (μ) is 80.
- The population standard deviation (σ) is 12.
- The sample size (n) is 95.
The mean of the sum of the samples (ΣX) is n*μ = 95*80
= 7600.
The standard deviation for the sum of the samples is √n * σ = √95 * 12
≈ 116.4.
These calculations allow you to determine probabilities and sums related to the samples' sum using the normal distribution.