Avril and Ben are surveying passing traffic, noting the number of occupants in each vehicle. Below is the table of results of their survey?

This is all about expectation - the chart has given us a sample and now we can use it to predict outcomes.

i - We need to know the total number of cars that are in the sample so that we can use that for the ratios and fractions in the following questions:

#44+37+22+10+6+1+4=124#

ii: has 2 occupants: #37/124#

iii: has four occupants: #10/124=5/62#

iv: has less than 4 - and so it's 1, 2, and 3 occupants: #105/124#

v: has at least 3 occupants - and so it's 3, 4, 5, 6, and more: #43/124#

vi: if 6,000 cars pass by, how many would be expected to have more than 3 occupants?

With our sample, we have #21/124# that have more than 3 occupants. So we'd expect (using a ratio of our sample #21/124# and comparing it to a ratio of what we'd expect to the total number of cars expected):

#21/124=x/6000#

#124x=21xx6000#

#x=(21xx6000)/124~=1016~=1020# rounded to the nearest 10

vii: if 3520 single passenger vehicles are anticipated on a single day, the total number of cars anticipated is (using a ratio of single passenger cars in our sample and comparing it to a ratio of anticipated single passenger cars to the total number of cars):

#44/124=3520/x#

#44x=124xx3520#

#x=(124xx3520)/44=9920#