The following contingency table provides frequencies for the preferred type of e
ID: 3330075 • Letter: T
Question
The following contingency table provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Here xx and yy represent missing values.
Age Group
Preferred Form of Exercise
Total
Running
Biking
Swimming
Under 35 years
157
121
79
xx
35 years or older
45
27
87
159
Total
yy
148
166
516
a) What is the probability of people preferring running?
b) Determine whether selecting an individual under 35 is independent of selecting an individual who prefers swimming.
Age Group
Preferred Form of Exercise
Total
Running
Biking
Swimming
Under 35 years
157
121
79
xx
35 years or older
45
27
87
159
Total
yy
148
166
516
Explanation / Answer
a) As the total people here are 516 out of which 166 prefer swimming, 148 prefers biking, then the number of people who prefers running would be computed as:
= 516 - 148 - 166 = 202
Now the probability of people preferring running is computed as:
= Number of people who prefers running / Total number of people
= 202 / 516
= 0.3915
Therefore 0.3915 is the required probability here.
b) P( swimming ) = 166 / 516 = 0.3217
Total people under 35 = 516 - 159 = 357
P( under 35 ) = 357 / 516 = 0.6919
Also, P( swimming and under 35 ) = 79 / 516 = 0.1531
P( swimming ) P( under 35) = 0.3217*0.6919 = 0.2226
Therefore we see that P( swimming and under 35 ) is not equal to P( swimming ) P( under 35)
Therefore the 2 events are not independent.
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