A city planner wants to estimate the average commute time (in minutes) for workers in a large city. If the standard deviation is estimated at $22$ minutes, how many workers must be surveyed to estimate the mean commute time within $5$ minutes with $90\%$ confidence?

Suppose the weights of apples in an orchard are normally distributed with a mean of $150$ grams and a standard deviation of $30$ grams. What effect does increasing the sample size have on the probability that the sample mean weight is close to $150$ grams? Explain your reasoning.