Question

Statisticians for a roadside assistance company interviewed 50,000 randomly selected United States (US) households. Of those, 15,595 reported that they had traveled 50 or more miles from home between December 23 and January 4. If there are 115,000,000 US households, approximately how many of them do the interviews suggest traveled 50 or more miles from home at that time?

Answer 1

35,868,500 people

Step-by-step explanation:

◉ We calculate the probability of those who traveled 50+ miles.

-Probability is the likelihood of success. n=50000, p=15595:

P ( X ≥ 50 ) = 15595 / 50000

= 0.3119

◉The US population is 115000000. We determine what fraction of the actual population traveled 50+ miles:

E (X) = np , N = 115000000 , P = 0.3119

= 0.3119 × 115000000

= 35868500

Hence, 35,868,500 people traveled 50+ miles.

Answer 2

Answer:

Approximately 36,000,000households traveled at that time.

Step-by-step explanation:

We can use proportions to solve this problem. It is only an approximation because of the possibility of sampling error.

(US HOUSEHOLDS making long trips/US HOUSEHOLDS)=(Interviewed Households making long trips/Interviewed Houses)

Let's use h to represent the approximate total number of US households that will be traveling at that time.

                 (h/115,000,000)=(15,595/50,000)

                 h=(15,000*115,000,000)/(50,000)

                 h=35,868,500

                 i.e, Aproximately 36,000,000households traveled at that time.