Final answer:
The mean of phone calls can be calculated by summing up all call lengths and dividing by the total number of calls. The probability of exceeding a certain number of calls, such as 20 long-distance calls, could be addressed using distribution models. Hypothesis testing is another statistical tool used to compare observed average call times against a hypothesized average.
Step-by-step explanation:
The question pertains to finding the mean of the lengths of 60 calls made by an executive during the last week of July. To calculate the mean, you would add up the lengths of all the calls and then divide by the number of calls, which is 60 in this case. However, your question seems to be more interested in the concept of probability concerning the number of phone calls made during peak times.
If we know that small companies have an average of 20 long-distance calls during the peak time of the day, the probability of making more than this average can be found using the Poisson or normal distribution, depending on the context and the data available. A similar process is used for hypothesis testing in the case of the organization that believes teenagers are currently spending more time on the phone than the previous average of 4.5 hours.
To conduct a hypothesis test, you would use the sample mean, the sample standard deviation, and the number of samples to calculate the test statistic. Then, using the appropriate distribution, you would determine the probability associated with this test statistic under the null hypothesis. If this probability (p-value) is less than the chosen significance level, you would reject the null hypothesis.