Multiple choice

Age Male Female Total $0-18$ year old $56$ $50$ $106$ $19-40$ years old $108$ $90$ $198$ $41-65$ years old $126$ $135$ $261$ $66+$ years old $90$ $96$ $185$ Total $380$ $370$ $750$ The age of a random sample of people from a population is summarized in the table above. The whole population consists of $31,000$ people. Mark the correct statement.

  1. We expect that there are $15,200$ females in the population
  2. We expect there to be $5580$ females $65$ years old and younger in the population
  3. We expect there to be $9300$ females between $19$ and $65$ years old in the population

  4. We cannot determine the number of females in the population with the information given
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Females aged 19 to 65 in the sample number 90 + 135 = 225. Scaling this to the population gives 225/750 x 31,000 = 9,300, so statement C is correct. The table has a small total inconsistency in the 66+ row, but it does not affect this calculation.

AI explanation

Using proportional scaling, the expected number of females between 19 and 65 years old in the population is the sample number of females in that age group multiplied by the total population and divided by the sample size. The sample contains 225 such females (90 plus 135). This gives 225 multiplied by 31000 and divided by 750, resulting in 9300 females.

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