Question

employees at a specific company were surveyed about whether they drive to work and whether they have kids. the results are shown below.
a) the company surveyed a total of employees.
b) the number of employees surveyed who drive to work is
c) the number of employees surveyed who drive to work and have kids is
d) the number of employees who dont drive and dont have kids is
e) the number of employees surveyed who drive, but do not have kids is
f) the number of employees surveyed who drive or have kids is
g) the percentage of employees surveyed who drive is

Explanation:

Step1: Calculate total employees

Add all the numbers in the Venn - diagram: \(22 + 30+8 + 5\).

$$22+30 + 8+5=65$$

Step2: Calculate employees who drive to work

Sum the parts of the 'Drive' circle: \(22+30\).

$$22 + 30=52$$

Step3: Calculate employees who drive to work AND have kids

This is the intersection of the two circles: \(30\).

Step4: Calculate employees who don't drive and don't have kids

This is the number outside both circles: \(5\).

Step5: Calculate employees who drive but do not have kids

This is the non - overlapping part of the 'Drive' circle: \(22\).

Step6: Calculate employees who drive OR have kids

Use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here \(n(A) = 52\) (drive), \(n(B)=30 + 8=38\) (have kids), \(n(A\cap B)=30\).

$$52+38 - 30=60$$

Step7: Calculate percentage of employees who drive

The formula for percentage is \(\frac{\text{Number of employees who drive}}{\text{Total number of employees}}\times100\). So \(\frac{52}{65}\times100\).

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Answer:

a) \(65\)
b) \(52\)
c) \(30\)
d) \(5\)
e) \(22\)
f) \(60\)
g) \(80\%\)