Based on census data and namm data, how many musicians are there?

Question

There are $115,226,802$ households in the US. $58$% of households have at least $1$ musician. $43$% have $2$ or more musicians. How many musicians are there?

Any help would be appreciated...

Answer 1

For a minimum, we have $15\%$ of the households with exactly one musician, so there are at least $115,226,802*(0.15+2*0.43)=116,379,070.02$ musicians. I'm not sure what to do with $0.02$ musician. There could be more, as there could be some households with more than two.

Answer 2

You can only narrow it down.

Assuming: * "2.61 persons per household" * 58% of household with at least 1 musician is exact-- 42% have no musician at all and likewise, * 43% percent have 2+ musicians and thus 57% have exactly 0 or 1 musician

Let T=115,226,802.

a.) 15%*T houses have exactly 1 musician --> 15%*T musicians

b.) 43%*T houses have at least 2 --> 43%*T*2 musicians

c.) 42%*T non-musicians

min.#musicians is 101%*T.

min.#non-musicians is 42%*T.

Total population is 100%*T*2.61=T*2.61=261%T

[261-(101+42)]%T=117%T=1.17*115,226,802 people can be anything.

In the expected case, it's all evenly split: there's 2.61 persons living in each and every household.

Then, it gets narrower:

From (a) above, 15%T musicians and 15%*T*1.61 non-musicians.

From (c) 42%*T*2.61 non-musicians.

the remaining 0.61*43%*T persons-- the rest of the household in 2+musician houses is vague, can't be told without more on how it is distributed beyond 2+/household.