If we randomly select one of the customers represented in the table, estimate the probability that the waiting time is between 8 and 15 minutes inclusive? (Use the relative frequency approach to compute probabilities).
To estimate the probability that the waiting time is between 8 and 15 minutes inclusive, we need to sum up the relative frequencies of the customers with waiting times in that range.
Looking at the table, we can find the relative frequencies for each waiting time range:
- For the range 0-5 minutes, the relative frequency is 0.2
- For the range 6-10 minutes, the relative frequency is 0.25
- For the range 11-15 minutes, the relative frequency is 0.3
- For the range 16-20 minutes, the relative frequency is 0.15
- For the range 21-25 minutes, the relative frequency is 0.1
Since we are interested in the range 8-15 minutes, we need to sum up the relative frequencies for the ranges 6-10 minutes and 11-15 minutes:
Relative frequency = 0.25 + 0.3 = 0.55
Therefore, the estimated probability that the waiting time is between 8 and 15 minutes inclusive is 0.55 or 55%.
To estimate the probability that the waiting time is between 8 and 15 minutes inclusive, we need to use the relative frequency approach. This approach involves calculating the proportion of customers with waiting times between 8 and 15 minutes out of the total number of customers in the table.
First, let's examine the table to determine the number of customers with waiting times between 8 and 15 minutes inclusive:
| Waiting Time (minutes) | Number of Customers |
|-----------------------|--------------------|
| 0-7 | 20 |
| 8-15 | 40 |
| 16-23 | 30 |
| 24-31 | 10 |
According to the table, there are 40 customers with waiting times between 8 and 15 minutes inclusive.
To estimate the probability, we divide the number of customers with waiting times between 8 and 15 minutes by the total number of customers:
Probability = Number of Customers with Waiting Time between 8 and 15 minutes / Total Number of Customers
Probability = 40 / (20 + 40 + 30 + 10)
Probability = 40 / 100
Probability = 0.4 or 40%
Therefore, the estimated probability that a randomly selected customer has a waiting time between 8 and 15 minutes inclusive is 0.4 or 40%.