Chapter 10.7, Problem 14IP

a.

To determine

To find: The probability of skateboarding being someone favourite sport.

Answer to Problem 14IP

The probability of skateboard as a favourite $37.50\%$ .

Explanation of Solution

Given information:

  $\begin{array}{l}\mathrm{BMX}=8\\ \mathrm{Inline}=6\\ \mathrm{MotoX}=4\\ \mathrm{SkateBoarding}=15\\ \mathrm{WakeBoarding}=7\end{array}$

Calculation:

The total numbers of responses was $=40$

So, P(Skateboard)

  $\begin{array}{l}=\frac{15}{40}\\ =\frac{3}{8}\\ =37.50\%\end{array}$

b.

To determine

To find: Predict the number will come close inline skating as their favourite sport .

Answer to Problem 14IP

The $120$ would be expected to choose inline skating.

Explanation of Solution

Given information:

  $\begin{array}{l}\mathrm{BMX}=8\\ \mathrm{Inline}=6\\ \mathrm{MotoX}=4\\ \mathrm{SkateBoarding}=15\\ \mathrm{WakeBoarding}=7\end{array}$

Students in the school are surveyed $=800$

Calculation:We use a proportion:

  $\begin{array}{l}\frac{n}{800}=\frac{6}{40}\\ 40n=4800\\ n=120\end{array}$ .

c.

To determine

To find:How many more students will prefer BMX than MotoX.

Answer to Problem 14IP

  $80$ More students would prefer BMX rather than MotoX

Explanation of Solution

Given information:

  $\begin{array}{l}BMX=8\\ Inline=6\\ MotoX=4\\ SkateBoarding=15\\ WakeBoarding=7\end{array}$

Surveyed students $=800$

Calculation:We use the same proportion to calculate the expected respondents

BMX

  $\begin{array}{l}\frac{n}{800}=\frac{8}{40}\\ n=\frac{8*800}{40}\\ n=160\end{array}$

MotoX

  $\begin{array}{l}\frac{n}{800}=\frac{4}{40}\\ n=\frac{4\times 800}{40}\\ n=80\end{array}$

  $160-80=80$ More students would prefer BMX rather than MotoX.