Albertoni Pizza Restaurant is facing a stiff competition from the new competing pizza restaurant guaranteeing pizza deliveries within 30 minutes or the pizza is given free. To answer this challenge, Albertoni wants to offer a 28-minute delivery guarantee. After a careful cost analysis, Albertoni has determined that such a guarantee would require an average delivery time of less than 26 minutes. She thought that this would limit the percentage of 'free pizzas' under the guarantee to less than 10.5% of all the deliveries, which she had figured to be the break-even point for such a promotion. To find out if the restaurant can meet these requirements, Albertoni collected data on the total delivery times and 'free pizzas' for a random sample of 64 orders within a month. The total delivery time includes the preparation-time, the wait-time, and the travel-time for the drivers. The sample data show an average total delivery time of 24.9 minutes with sample standard deviation of 1.2 minutes. The data also show that 3 out of the 64 orders resulted in 'free pizza' deliveries because they took longer than 28 minutes to deliver. Albertoni is using a non-conventional confidence level of 96% in her estimates. Please answer the following questions using the information given in this problem. a. Please calculate and interpret the 96% confidence interval for the mean total delivery time of pizzas for the Albertoni Restaurant. Please show the necessary steps.

The 96% confidence interval for the mean total delivery time of pizzas for the Albertoni Restaurant is (24.5 minutes, 25.3 minutes). This interval provides a range of values within which we can estimate the true population mean with 96% confidence.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

First, we need to calculate the critical value. Since Albertoni is using a non-conventional confidence level of 96%, we need to find the z-score associated with a 96% confidence level. Using a standard normal distribution table or a statistical software, we find that the critical value is approximately 2.05.

Next, we calculate the standard error using the formula:

Standard Error = Sample Standard Deviation / √(Sample Size)

In this case, the sample standard deviation is 1.2 minutes, and the sample size is 64. Therefore, the standard error is approximately 0.15 minutes.

Now, we can calculate the confidence interval:

Confidence Interval = 24.9 ± (2.05 * 0.15) = (24.5 minutes, 25.3 minutes)

We are 96% confident that the true mean total delivery time of pizzas for the Albertoni Restaurant falls within the range of 24.5 minutes to 25.3 minutes.

This means that if we were to take multiple samples and calculate confidence intervals, approximately 96% of those intervals would contain the true population mean.

To know more about interval, refer here:

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