A questionnaire has determined that 20% of the residents of Flaugamuck County own an iPod. Furthermore, 80% of these iPod owners are under 30 years of age, whereas 20% are 30 or older. Only 35% of the people who don't own iPods are under 30 years of age. What percentage of the residents who are 30 or older own iPods?

Question

Evelyn Clay

Mathematics

6 October, 17:31

A questionnaire has determined that 20% of the residents of Flaugamuck County own an iPod. Furthermore, 80% of these iPod owners are under 30 years of age, whereas 20% are 30 or older. Only 35% of the people who don't own iPods are under 30 years of age. What percentage of the residents who are 30 or older own iPods?

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Answers (1)

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Gilbert Estes · Answer 1

P = 7.14%

The percentage of those 30 years or older that own an ipod is 7.14%

Step-by-step explanation:

Given;

Percentage of ipod owners Pi = 20%

Percentage who don't own ipod Pd = 100-20 = 80%

For age 30 or older;

Percentage of ipod owners who belong to this group

Po = 20% of Pi

Percentage who don't have an ipod but belong to this group Pu = 100-35% = 65% of Pd

The percentage of those 30 years or older that own an ipod is;

P = Po / (Po+Pu) * 100%

Po = 20% of Pi = 20% of 20% = 0.2*20 = 4%

Pu = 65% of Pd = 65% of 80% = 0.65*80% = 52%

Substituting the values;

P = 4 / (4+52) * 100%

P = 7.14%