Solved Step by Step with Explanation Stats: Sampling, Probabilities & Graphs

Question

Solved Step by Step with Explanation Stats: Sampling, Probabilities & Graphs

When you take multiple random samples from a population and calculate the mean of each sample, those means form a distribution known as the sampling distribution of means. This distribution has three key characteristics:

1. Location (Central Tendency): The mean of the sampling distribution of means is equal to the true population mean. In mathematical notation: µ(x̄) = µ (population mean = sample mean).

In this case:

- Population Mean (µ) = 12 hours

z = (14 - 12) / (5 / √30) ≈ 2.68

Using a standard normal distribution table or calculator, find the probability associated with z = 2.68. This probability represents the likelihood of obtaining a sample mean greater than 14 hours from a non-normally distributed population.

- Desired Value (x) = 22.95 hours

Calculate the z-score: