Question

Superpowers A total of 415 children from the United Kingdom and the United States who completed a survey in a recent year were randomly selected. Each student’s country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to read minds). The data are summarized in the following table.

(a) What proportion of students in the sample are from the United States?

(b) Find the distribution of superpower preference for the students in the sample using relative frequencies.

(c) What percent of students in the sample are from the United Kingdom and prefer telepathy as their superpower preference?

Short answer

Part (a) 43/83 or 0.5181.

Part (b)

$$\begin{gathered} \mathrm{Fly}=23.86\%,\mathrm{Freeze}\mathrm{time}=23.13\%,\mathrm{Invisibility}=16.14\% \\ \mathrm{Superstrength}=10.36\%,\mathrm{Telepathy}26.51\% \end{gathered}$$

Part (c) 10.60%

Step-by-step solution

Part (a) Step 1. Given information.

The given table is:

Part (a) Step 2. Determine the proportion of students in the sample from the United States 

Total students from the US:

$45+44+37+23+66=215$

Total students both from UK and US:

$54+52+30+20+44+45+44+37+23+66=415$

The proportion of US students in the sample is:

$\frac{215}{415}=\frac{43}{83}\mathrm{or}\approx 0.5181$

Part (b) Step 1.  Find the distribution of superpower preference.

	U.K.	U.S.	Row Total	Distribution of superpower preference
Fly	54	45	99	$\frac{99}{415}\approx 0.2386\mathrm{or}23.86\%$
Freeze time	52	44	96	$\frac{96}{415}\approx 0.2313\mathrm{or}23.13\%$
Invisibility	30	37	67	$\frac{67}{415}\approx 0.1614\mathrm{or}16.14\%$
Superstrength	20	23	43	$\frac{43}{415}\approx 0.1036\mathrm{or}10.36\%$
Telepathy	44	66	110	$\frac{110}{415}\approx 0.2651\mathrm{or}26.51\%$

Part (c) Step 1. Determine the percentage of students from the United Kingdom who prefer telepathy.

Number of Students from the U.K that prefers telepathy are 44.

Their percentage is:

$\frac{44}{415}=0.1060\mathrm{or}10.60\%$