To solve this problem, I will follow these steps:

1. Determine the proportion of service times less than or equal to 50 seconds:

   • Analyze the data provided in the file (Restaurant.xlsx) to count how many of the 50 service times meet the condition $\leq 50$ seconds.
   • Calculate the sample proportion $\hat{p}$.

2. Calculate a 90% confidence interval:

   • Use the formula for a confidence interval for a population proportion: $\hat{p} \pm Z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$ where:
     • $Z$ is the critical value corresponding to a 90% confidence level ($Z = 1.645$).
     • $n$ is the sample size (50 in this case).

3. Evaluate if the 90% confidence interval supports the manager’s goal:

   • Check if at least 80% of the service times ($p = 0.8$) fall within the confidence interval.
   • Provide recommendations accordingly.

I’ll start by processing the data file to extract the necessary information. Please upload the "Restaurant.xlsx" file so I can proceed.