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Home modifications for wheelchair users. The American
Chapter 3, Problem 115SE(choose chapter or problem)
Problem 115SE
Home modifications for wheelchair users. The American Journal of Public Health (Jan. 2002) reported on a study of elderly wheelchair users who live at home. A sample of 306 wheelchair users, age 65 or older, were surveyed about whether they had an injurious fall during the year and whether their home features any one of five structural modifications: bathroom modifications, widened doorways/ hallways, kitchen modifications, installed railings, and easyopen doors. The responses are summarized in the accompanying table. Suppose we select, at random, one of the 306 surveyed wheelchair users.
Home Features |
Injurious Fall(s) |
No Falls |
Totals |
All 5 |
2 |
7 |
9 |
At least 1 but not all |
26 |
162 |
188 |
None |
20 |
89 |
109 |
Totals |
48 |
258 |
306 |
Source: Based on Berg, K., Hines, M., & Allen, S. “Wheelchair users at home: Few home modifications and many injurious falls,” American Journal of Public Health, Vol. 92, No. 1, Jan. 2002 (Table 1).
a. Find the probability that the wheelchair user had an injurious fall.
b. Find the probability that the wheelchair user had all five features installed in the home.
c. Find the probability that the wheelchair user had no falls and none of the features installed in the home.
d. Given the wheelchair user had all five features installed, what is the probability that the user had an injurious fall?
e. Given the wheelchair user had none of the features installed, what is the probability that the user had an injurious fall?
Questions & Answers
QUESTION:
Problem 115SE
Home modifications for wheelchair users. The American Journal of Public Health (Jan. 2002) reported on a study of elderly wheelchair users who live at home. A sample of 306 wheelchair users, age 65 or older, were surveyed about whether they had an injurious fall during the year and whether their home features any one of five structural modifications: bathroom modifications, widened doorways/ hallways, kitchen modifications, installed railings, and easyopen doors. The responses are summarized in the accompanying table. Suppose we select, at random, one of the 306 surveyed wheelchair users.
Home Features |
Injurious Fall(s) |
No Falls |
Totals |
All 5 |
2 |
7 |
9 |
At least 1 but not all |
26 |
162 |
188 |
None |
20 |
89 |
109 |
Totals |
48 |
258 |
306 |
Source: Based on Berg, K., Hines, M., & Allen, S. “Wheelchair users at home: Few home modifications and many injurious falls,” American Journal of Public Health, Vol. 92, No. 1, Jan. 2002 (Table 1).
a. Find the probability that the wheelchair user had an injurious fall.
b. Find the probability that the wheelchair user had all five features installed in the home.
c. Find the probability that the wheelchair user had no falls and none of the features installed in the home.
d. Given the wheelchair user had all five features installed, what is the probability that the user had an injurious fall?
e. Given the wheelchair user had none of the features installed, what is the probability that the user had an injurious fall?
ANSWER:
Solution:
Step 1 of 3:
A sample of 306 wheelchair users, age 65 or older, were surveyed about whether they had an injurious fall during the year and whether their home features an y one of the five structural modifications.
Home Features |
Injurious Fall(s) |
No Falls |
Totals |
All 5 |
2 |
7 |
9 |
At least 1 but not all |
26 |
162 |
188 |
None |
20 |
89 |
109 |
Totals |
48 |
258 |
306 |
We have to find,
- The probability that the wheelchair user had an injurious fall.
- The probability that the wheelchair user had all five features installed in the home.
- The probability that the wheelchair user had no falls and none of the features installed in the home.
- The probability that the user had an injurious fall, given that the wheelchair user had all five features installed.
- The probability that the user had an injurious fall, given that the wheelchair used had none of the features installed.