Final answer:
The exact probability cannot be calculated without specific values. It involves using the standard error to convert the range to z-scores, and then looking up these z-scores in a z-table or using statistical software to find the probabilities.
Step-by-step explanation:
The probability that a simple random sample of unemployed individuals will provide a sample mean within 1 week of the population mean depends on several factors, including the population standard deviation and the actual sample mean. Since these are not provided, we cannot calculate the exact probability. However, if we assume the distribution of the sample means is approximately normal due to the Central Limit Theorem, we can use the standard normal distribution to find this probability.
To calculate the probability that a sample mean falls within a certain range of the population mean, we would use the formula for the standard error of the mean, which is the population standard deviation divided by the square root of the sample size. We would then convert the range around the mean (i.e., 1 week or 1⁄2 week) to z-scores and use a z-table or statistical software to find the probabilities that the sample mean falls within those z-scores.