Question

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.

4

6

11

12

5

2

5

19

11

8

6

8

15

21

6

9

6

14

19

3

1. Fill in the frequency (to the nearest whole number) and the relative frequency (2 decimals) values below.
   

   Waiting Time	Frequency	Relative Frequency
   0-4
   5-9
   10-14
   15-19
   20-24
   (Total)

   
   
2. Fill in the cumulative frequency (to the nearest whole number) and the cumulative relative frequency (2 decimals) values below.
   

   Waiting Time	Cumulative Frequency	Cumulative Relative Frequency
   Less than or equal to 4
   Less than or equal to 9
   Less than or equal to 14
   Less than or equal to 19
   Less than or equal to 24

   
   
3. What proportion of patients needing emergency service wait 19 minutes or less?

Answer 1

Answer)

A)

Waiting time frequency. Relative frequency

0-4. 3. (3/20) = 0.15

5-9. 9. (9/20) = 0.45

10-14. 4. (4/20) = 0.2

15-19. 3. (3/20) = 0.15

20-24. 1. (1/20) = 0.05

Total. 20. 1

As there are 3 data values in between 0 and 4

(2, 3, 4) therefore, frequency of 0-4 is 3

And relative frequency is equal to frequency/sum of frequencies

B)

Waiting time. Cumulative cumulative relative

Less than or equal to 4. 3. 0.15

Less than or equal to 9. (3+9) = 12. (0.15+0.45) = 0.6

Less than or equal to 14. (12+4) = 16. (0.6+0.2) = 0.8

Less than or equal to 19. (16+3) = 19 (0.8+0.15) = 0.95

Less than or equal to 24. (19+1) = 20. (0.95+0.05) = 1

C)

Proportion = favorable/total

Total = sum of frequencies = 20

Favorable = less than 19 = 3+9+4+3 = 19

Proportion = 19/20 = 0.95