Chapter 1: Q 24. (page 26)

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?

Expert verified

Part (a) 43/83 or 0.5181.

Part (b)

$Fly = 23.86 %, Freeze time = 23.13 %, Invisibility = 16.14 % Superstrength = 10.36 %, Telepathy 26.51 %$

Part (c) 10.60%

Step by step solution

The given table is:

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:

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

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