Question

A choral conductor has 1542 singers in her choir, some of them are professional singers. The conductor wants to estimate what percentage of singers are professional, but can't ask all 1542, so she instead asks 650 singers in front and finds 19 who are professionals.

Answer 1

The value is
`\r p  =  2.9\%`

Explanation:

From the question we are told that

The number of singers is
`N  =  1542`

The sample size is
`n  =  650`

The number the number of singers who are professional is k = 19

The proportion of professional singers is mathematically represented as

`p  =  (k)/(n)`

=>
`p  =  (19)/(650)`

=>
`p  =  0.029`

The percentage estimate of singers who are professional is

`\r p  =  100 * 0.029`

`\r p  =  2.9\%`