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:
(c) The probability that the food truck averages more than $\$ 900$ of revenue over the span of 5 days.
Answer
Final Answer: The probability that the food truck averages more than $900 of revenue over the span of 5 days is approximately \(\boxed{0.1007}\).
Step 1 ：The problem is asking for the probability that the average revenue over 5 days is more than $900. This is a problem of normal distribution.
Step 2 ：The mean of the distribution is $800 and the standard deviation is $175.
Step 3 ：Since we are considering the average over 5 days, the mean will still be $800 but the standard deviation will be \(\frac{175}{\sqrt{5}}\) because the standard deviation of the mean of a sample is the standard deviation of the population divided by the square root of the sample size.
Step 4 ：We need to calculate the z-score for $900 which is \(\frac{900-800}{\frac{175}{\sqrt{5}}}\) and then find the area to the right of this z-score in the standard normal distribution.
Step 5 ：The z-score is approximately 1.2777531299998799.
Step 6 ：The probability is approximately 0.10066824264370045.
Step 7 ：Final Answer: The probability that the food truck averages more than $900 of revenue over the span of 5 days is approximately \(\boxed{0.1007}\).
