Question

assign biggest decrease to the biggest decrease in waiting time between two consecutive eruptions. for example, the third eruption occurred after 74 minutes and the fourth after 62 minutes, so the decrease in waiting time was 74 - 62

Answer 1

The subject of this question is Mathematics. To find the biggest decrease in waiting time between two consecutive eruptions, you need to compare the waiting times of the eruptions. For example, if the waiting time for the third eruption is 74 minutes and the waiting time for the fourth eruption is 62 minutes, the decrease in waiting time would be 12 minutes.

Step-by-step explanation:

The subject of this question is Mathematics. The question asks you to assign the biggest decrease in waiting time between two consecutive eruptions. To find this, you need to compare the waiting times of two consecutive eruptions. For example, if the waiting time for the third eruption is 74 minutes and the waiting time for the fourth eruption is 62 minutes, the decrease in waiting time would be 74 - 62 = 12 minutes.

Answer 2

The question involves finding the biggest decrease in waiting times from provided data, interpreting a scatter plot for wait times between durations of eruptions, calculating probabilities with the exponential distribution, and understanding waiting times using a uniform distribution.

Step-by-step explanation:

The assignment appears to be focused on data analysis and probability, with a scenario involving wait times between eruptions or customer arrivals. In this context, assigning the biggest decrease in waiting time would involve analyzing a set of data points and calculating the differences between consecutive waiting times to determine the largest decrease. For instance, you've given an example where the time decreased from 74 to 62 minutes, which is a decrease of 12 minutes. If you want to find the biggest decrease, you'll need a set of such waiting times, calculate the differences for each consecutive pair, and then identify the largest decrease from those differences.

When interpreting the scatter plot in Figure 0.5, you're looking at the correlation between eruption durations and waiting times. If asked to interpolate for wait times between eruptions lasting between 2.5 to 4.0 minutes, you'd examine where those durations would fall on the X-axis (duration of eruptions) and estimate their corresponding wait times on the Y-axis (time between eruptions) based on the linear trend observed in the scatter plot.

Regarding the exponential distribution mentioned in Example 5.11, if on average 30 customers arrive per hour, it implies one arrives every two minutes. Thus, it would take approximately six minutes for three customers to arrive. To find the probability that the next customer arrives in less than one minute, the exponential distribution formula would be employed.

In the last exercise about the uniform distribution of waiting times for a rural bus, with times ranging from zero to 75 minutes, calculating whether a sample average wait time of less than 30 minutes is surprising would involve determining if such a result is likely given the known distribution. This could involve calculating the expected mean and variance, and then seeing how a mean of 30 minutes compares to these.