Question

1. 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 students 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). their data are summarized in the following table.

superpower	country	u.k.	u.s.
freeze time		52	44
invisibility		30	37
superstrength		20	23
telepathy		44	66

(a) what proportion of students in the sample are from the united states?
(b) find the distribution of super - power 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?

Explanation:

Step1: Calculate total number of students

The total number of students is the sum of all values in the table. So, \(54 + 45+52 + 44+30+37+20+23+44+66=415\).

Step2: Calculate proportion of students from US

The number of students from the US is \(45 + 44+37+23+66 = 215\). The proportion of students from the US is \(\frac{215}{415}=\frac{43}{83}\approx0.518\).

Step3: Calculate relative - frequencies for super - power preference

For flying: \(\frac{54 + 45}{415}=\frac{99}{415}\approx0.239\); for freezing time: \(\frac{52+44}{415}=\frac{96}{415}\approx0.231\); for invisibility: \(\frac{30 + 37}{415}=\frac{67}{415}\approx0.162\); for super - strength: \(\frac{20+23}{415}=\frac{43}{415}\approx0.104\); for telepathy: \(\frac{44 + 66}{415}=\frac{110}{415}=\frac{22}{83}\approx0.265\).

Step4: Calculate percentage of students from UK and prefer telepathy

The number of students from the UK who prefer telepathy is 44. The percentage is \(\frac{44}{415}\times100=\frac{4400}{415}\approx10.6\%\).

Answer:

(a) \(\frac{43}{83}\approx0.518\)
(b) Flying: \(\frac{99}{415}\approx0.239\), Freezing time: \(\frac{96}{415}\approx0.231\), Invisibility: \(\frac{67}{415}\approx0.162\), Super - strength: \(\frac{43}{415}\approx0.104\), Telepathy: \(\frac{22}{83}\approx0.265\)
(c) \(\frac{4400}{415}\approx10.6\%\)