Question

Patient Waiting Times. A doctor's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period. Use classes of 0−4,5−9, and so on in the following: a. Show the frequency distribution. b. Show the relative frequency distribution. c. Show the cumulative frequency distribution. d. Show the cumulative relative frequency distribution. E) What proportion of patients needing emergency service wait 9 minutes or less?

Answer 1

To generate random numbers using the given variables a, X0, C, and m, use the formula (a * X0 + C) % m. Then, use the K-S test to compare the empirical and theoretical distribution functions.

Step-by-step explanation:

To generate random numbers using the given variables a, X0, C, and m, you can use the formula:

X1 = (a * X0 + C) % m

X2 = (a * X1 + C) % m

...

Following this formula, you can generate eight random numbers:

X1 = (11 * 1 + 7) % 50 = 18

X2 = (11 * 18 + 7) % 50 = 15

X3 = (11 * 15 + 7) % 50 = 22

...

The generated random numbers are 18, 15, 22, ...

The K-S test measures the maximum distance between the empirical distribution function of the generated random numbers and the theoretical distribution function. Without the values of D-max and D+ max provided, it is not possible to determine the correct option from the given choices.

Answer 2

To create a frequency distribution, relative frequency distribution, cumulative frequency distribution, and cumulative relative frequency distribution for the waiting times of patients needing emergency service, follow these steps:

Step 1: Organize the data into classes (intervals). In this case, we'll use classes of 0-4, 5-9, 10-14, and so on.

Step 2: Count the frequency of data points within each class.

Step 3: Calculate the relative frequency, which is the frequency divided by the total number of data points.

Step 4: Calculate the cumulative frequency, which is the sum of frequencies up to and including the current class.

Step 5: Calculate the cumulative relative frequency, which is the cumulative frequency divided by the total number of data points.

Let's calculate these for your data:

Assuming the waiting times data is as follows (in minutes):

[3, 7, 8, 12, 14, 17, 19, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70]

a. Frequency Distribution:

| Class Interval | Frequency |

|----------------|-----------|

| 0-4 | 1 |

| 5-9 | 2 |

| 10-14 | 2 |

| 15-19 | 3 |

| 20-24 | 2 |

| 25-29 | 2 |

| 30-34 | 3 |

| 35-39 | 2 |

| 40-44 | 2 |

| 45-49 | 1 |

| 50-54 | 1 |

| 55-59 | 1 |

| 60-64 | 1 |

| 65-69 | 1 |

| 70-74 | 1 |

b. Relative Frequency Distribution:

To find the relative frequency, divide the frequency in each class by the total number of data points (20 in this case).

| Class Interval | Relative Frequency |

|----------------|--------------------|

| 0-4 | 0.05 |

| 5-9 | 0.10 |

| 10-14 | 0.10 |

| 15-19 | 0.15 |

| 20-24 | 0.10 |

| 25-29 | 0.10 |

| 30-34 | 0.15 |

| 35-39 | 0.10 |

| 40-44 | 0.10 |

| 45-49 | 0.05 |

| 50-54 | 0.05 |

| 55-59 | 0.05 |

| 60-64 | 0.05 |

| 65-69 | 0.05 |

| 70-74 | 0.05 |

c. Cumulative Frequency Distribution:

To find the cumulative frequency, sum the frequencies up to and including the current class.

| Class Interval | Cumulative Frequency |

|----------------|----------------------|

| 0-4 | 1 |

| 5-9 | 3 |

| 10-14 | 5 |

| 15-19 | 8 |

| 20-24 | 10 |

| 25-29 | 12 |

| 30-34 | 15 |

| 35-39 | 17 |

| 40-44 | 19 |

| 45-49 | 20 |

| 50-54 | 21 |

| 55-59 | 22 |

| 60-64 | 23 |

| 65-69 | 24 |

| 70-74 | 25 |

d. Cumulative Relative Frequency Distribution:

To find the cumulative relative frequency, divide the cumulative frequency by the total number of data points (20).

| Class Interval | Cumulative Relative Frequency |

|----------------|------------------------------|

| 0-4 | 0.05 |

| 5-9 | 0.15 |

| 10-14 | 0.25 |

| 15-19 | 0.40 |

| 20-24 | 0.50 |

| 25-29 | 0.60 |

| 30-34 | 0.75 |

| 35-39 | 0.85 |

| 40-44 | 0.95 |

| 45-49 | 1.00 |

| 50-54 | 1.05 |

| 55-59 | 1.10 |

| 60-64 | 1.15 |

| 65-69 | 1.20 |

| 70-74 | 1.25 |

e. To find the proportion of patients needing emergency service who wait 9 minutes or less, you can look at the cumulative relative frequency for the class interval "0-9," which is 0.15. This means that 15% of patients wait 9 minutes or less for emergency service.

Step-by-step explanation: