Question

3 scientists give two different treatments to people who have the flu and determine if their health improves. the results for the experiment are in the two - way table.
treatment 1treatment 2
improved health2325
no improvement1735
a. what percentage of people receiving treatment 1 had improved health?____
b. what percentage of people receiving treatment 2 had improved health?____
4 a group of people are surveyed about whether they enjoy dancing or not and whether they listen to music while doing chores or not.
listens to music while doing choresdoes not listen to music while doing chores
enjoys dancing82105
does not enjoy dancing141
which value could go in the blank cell so that the percentage of people who do not listen to music while doing chores and do not enjoy dancing is 37.5%?
a 63
b 82
c 175
d 205

Explanation:

Step1: Calculate total number of people for treatment 1

Total for treatment 1 = \(23 + 17=40\)

Step2: Calculate percentage for treatment 1

Percentage \(=\frac{23}{40}\times100 = 57.5\%\)

Step3: Calculate total number of people for treatment 2

Total for treatment 2 = \(25+35 = 60\)

Step4: Calculate percentage for treatment 2

Percentage \(=\frac{25}{60}\times100\approx41.7\%\)

Step5: For question 4

Let the value in the blank cell be \(x\). Total number of people who do not listen to music while doing chores \(=105 + x\). Total number of people surveyed \(=82 + 105+141+x=328 + x\).
We know that \(\frac{x}{105 + x}=0.375\) (since \(37.5\%=0.375\))

$$x = 0.375\times(105 + x)$$

$$x=0.375\times105+0.375x$$

$$x-0.375x = 39.375$$

$$0.625x=39.375$$

$$x = 63$$

Answer:

a. \(57.5\%\)
b. \(41.7\%\)

1. A. \(63\)