Researchers at Jackson Hospital asked 40 randomly selected patients about their sleep habits. Sixteen reported sleeping 8 hours or more each night. If there are 700 patients in the hospital, estimate the number of patients who sleep 8 hours or more each night.
A. 140
B. 160
C. 180
D. 280
We can set up a proportion to solve for the estimated number of patients who sleep 8 hours or more:
16/40 = x/700
Simplifying this proportion, we get:
0.4 = x/700
To solve for x, we can multiply both sides by 700:
x = 0.4 * 700
x = 280
Therefore, the estimated number of patients who sleep 8 hours or more each night is 280, which is option D.
To estimate the number of patients who sleep 8 hours or more each night, we can use the ratio of the 40 randomly selected patients to the total number of patients in the hospital.
16 out of 40 patients reported sleeping 8 hours or more each night.
If we assume this ratio holds true for the entire population, we can set up a proportion:
16/40 = x/700
To solve for x (the number of patients who sleep 8 hours or more each night), we can cross-multiply:
40x = 16 * 700
40x = 11200
Divide both sides by 40 to solve for x:
x = 11200/40
x = 280
Therefore, the estimated number of patients who sleep 8 hours or more each night is 280.
The answer is D. 280.