the table below shows the results of a random sample of 160 teenagers.\n| |like to surf|do not like to…

the table below shows the results of a random sample of 160 teenagers.\n| |like to surf|do not like to surf|total|\n|--|--|--|--|\n|boys|80|25|105|\n|girls|45|10|55|\n|total|125|35|160|\nbased on the information given, which of the following statements are true? select all that apply.\n□ 66% of the participants were boys.\n□ 35% of the participants do not like to surf.\n□ $\frac{80}{105}$ of the boys like to surf.\n□ $\frac{10}{35}$ of the participants who do not like to surf were girls.\n□ the proportion of boys who like to surf is greater than the proportion of girls who like to surf.

the table below shows the results of a random sample of 160 teenagers.\n| |like to surf|do not like to surf|total|\n|--|--|--|--|\n|boys|80|25|105|\n|girls|45|10|55|\n|total|125|35|160|\nbased on the information given, which of the following statements are true? select all that apply.\n□ 66% of the participants were boys.\n□ 35% of the participants do not like to surf.\n□ $\frac{80}{105}$ of the boys like to surf.\n□ $\frac{10}{35}$ of the participants who do not like to surf were girls.\n□ the proportion of boys who like to surf is greater than the proportion of girls who like to surf.

Answer

Explanation:

Step1: Calculate percentage of boys

Number of boys is 105 out of 160 participants. Percentage of boys = $\frac{105}{160}\times100\approx65.625%\neq66%$.

Step2: Calculate percentage of non - surfers

Number of non - surfers is 35 out of 160 participants. Percentage of non - surfers = $\frac{35}{160}\times 100 = 21.875%\neq35%$.

Step3: Calculate proportion of boys who like to surf

Number of boys who like to surf is 80 out of 105 boys. Proportion is $\frac{80}{105}=\frac{16}{21}$.

Step4: Calculate proportion of girls among non - surfers

Number of girls among non - surfers is 10 out of 35 non - surfers. Proportion is $\frac{10}{35}=\frac{2}{7}$.

Step5: Calculate proportion of girls who like to surf

Number of girls who like to surf is 45 out of 55 girls. Proportion is $\frac{45}{55}=\frac{9}{11}$. Compare with proportion of boys who like to surf $\frac{80}{105}=\frac{16}{21}$. Cross - multiply: $16\times11 = 176$ and $9\times21=189$, so $\frac{16}{21}<\frac{9}{11}$, the statement about proportion is false.

Answer:

$\frac{80}{105}$ of the boys like to surf, $\frac{10}{35}$ of the participants who do not like to surf were girls.