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Using Vieta's Theorem, it is found that c = 72.
<h3>What is the Vieta Theorem?</h3>- Suppose we have a quadratic equation, in the following format:
- The roots are p and q.
The Theorem states that:
In this problem, the polynomial is:
Hence the coefficients are .
Since the difference of the solutions is 1, we have that:
Then, from the first equation of the Theorem:
Now, from the second equation:
To learn more about Vieta's Theorem, you can take a look at brainly.com/question/23509978
Using the t-distribution, as we have the standard deviation for the sample, it is found that there is a significant difference between the wait times for the two populations.
<h3>What are the hypothesis tested?</h3>At the null hypothesis, we test if there is no difference, that is:
At the alternative hypothesis, it is tested if there is difference, that is:
For each sample, we have that:
For the distribution of differences, we have that:
It is given by:
In which is the value tested at the null hypothesis.
Hence:
Considering a one-tailed test, as stated in the exercise, with 100 - 1 = 99 df, using a t-distribution calculator, the p-value is of 0.014.
Since the p-value is less than the significance level of 0.05, it is found that there is a significant difference between the wait times for the two populations.
More can be learned about the t-distribution at brainly.com/question/16313918