Final answer:
To determine the probability of observing a sample mean of 20 or more from a sample of size 39, calculate the z-score using the given formula and find the probability using a standard normal distribution table or calculator.
Step-by-step explanation:
To determine the probability of observing a sample mean of 20 or more from a sample of size 39, we need to find the z-score and use it to calculate the probability using the standard normal distribution. Let's use the formula for calculating the z-score: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.
Given that the population mean (μ) is 22, the standard deviation (σ) is 15, and the sample size (n) is 39, we can plug these values into the formula: z = (20 - 22) / (15 / √39).
After calculating the z-score, we can find the probability using a standard normal distribution table or a calculator. The probability will be the area to the right of the z-score. In this case, we are looking for the probability of observing a sample mean of 20 or more, so we need to find the area to the right of the z-score.