After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30. a) What percent of the respondents were under 30 and did not snore? b) Is snoring independent of age? Explain.

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21-02-2020
Mathematics

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After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30. a) What percent of the respondents were under 30 and did not snore? b) Is snoring independent of age? Explain.

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tochinwachukwu33 tochinwachukwu33 · Answer 1 · 2020-02-23T07:24:54+01:00

Answer:

A. 73.91% of the respondents were under 30 and did not snore

B. From the data, snoring is not independent of age as most of the people that snored were above 30 years

Step-by-step explanation:

A. The first step is to convert all population groups represented as percentages to figures. This will help make things clearer.

Total number of adults that partook in the survey = 995 adults

Number of adults above 30 years = 81.5% of 995 = [tex]\frac{81.5}{100}[/tex]×995 = 810.925 ≈ 811 persons ( in population studies, whole numbers are usually used since we can't count a fraction of a human being).

Number of adults below 30 years = 995 - 811 = 184 adults.

Number of all adults that snored = 36.8% of 995

= [tex]\frac{36.8}{100}[/tex] × 995 ≈ 366 adults snored in total

Of the total 995, 32% of the people that snored were over 30.

Number of snorers that were over 30 are [tex]\frac{32}{100}[/tex]×995 ≈ 318 adults

Snorers under 30 years = 366 - 318 = 48 adults

Since 48 adults that are under 30 snore, adults under 30 that don't snore can be got by

Total number of people under 30 years - snorers under 30 years

= 184 - 48 = 136 adults under 30 years do not snore.

converting this to a percentage we have [tex]\frac{136}{184}[/tex] × 100 = 73.91 %

Hence, 73.91 % of the respondents under 30 years did not snore

B. From the data, snoring is not independent of age as most of the people that snored were above 30 years. Snoring is related to the age. This is because that the most of the younger adults did not snore, while more of the older adults snored.