Final answer:
The probability that the sample mean is within 3 units is 90%.
Step-by-step explanation:
The probability that the sample mean is within 3 units can be determined by finding the confidence interval. If we assume a normal distribution, we can use the concept of z-scores to find the probability. For a two-sided 95% confidence interval, we have 2.5% in each tail of the distribution. This means that the probability that the sample mean is within 3 units is 95% - (2.5% + 2.5%) = 90%.