Final answer:
The probability question about the average number of residents requires using the Central Limit Theorem to find the Z-score for a sample mean of 22.6 thousand; then look up that Z-score's corresponding probability in the standard normal distribution to find the area to the right of the Z-value.
Step-by-step explanation:
To solve this, we can use the Central Limit Theorem since the sample size is large (>30). The theorem tells us that the distribution of the sample means will be approximately normally distributed if the sample size is large enough, even if the population distribution is not normal. Our goal is to find the probability that the sample mean is greater than 22.6 thousand residents.
The sampling distribution of the mean will have a mean equal to the population mean (20 thousand) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (11.7 / √45). This standard deviation is the standard error of the mean. We can use this to calculate the Z-score for the sample mean of 22.6 thousand.
The Z-score is given by (X - μ) / (σ / √ n), where X = 22.6, μ = 20, σ = 11.7, and n = 45. After calculating the Z-score, we look up the corresponding probability in the standard normal distribution table. The requested probability is the area to the right of this Z-value in the normal distribution curve.
To find this, we use a calculator or statistical software, because the standard normal distribution table is not able to give us the precise value necessary for this question. Therefore, without the exact calculation, we can only describe the process, and cannot provide the specific letter answer from the options given.