Extra Credit: Suppose that the amount of revenue that a food truck makes per day is normally distributed with a mean of $\$ 800$ and a standard deviation of $\$ 175$. Calculate the following probabilities: (b) Assuming each day is independent, the probability that the food truck makes more than $\$ 900$ of revenue for 5 days in a row. (c) The probability that the food truck averages more than $\$ 900$ of revenue over the span of 5 days.

Step 1 ：First, we need to calculate the z-score for a single day's revenue of $900. The z-score formula is \((X - μ) / σ\), where X is the value we're interested in ($900), μ is the mean ($800), and σ is the standard deviation ($175). This gives us a z-score of approximately 0.57.

Step 2 ：Next, we use a z-table to find the probability that a value is greater than our z-score. However, most z-tables only give the probability that a value is less than a certain z-score, so we'll need to subtract our result from 1 to get the probability that a value is greater than our z-score. This gives us a probability of approximately 0.28 for a single day.

Step 3 ：Since each day is independent, we can then raise this probability to the power of 5 to get the probability that the food truck makes more than $900 of revenue for 5 days in a row. This gives us a final probability of approximately 0.0018.

Step 4 ：Thus, the probability that the food truck makes more than $900 of revenue for 5 days in a row is approximately \(\boxed{0.0018}\).