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Math

QuestionAnalyze 400 Saturday night accidents. Find proportions related to vehicles and alcohol involvement.

Studdy Solution

STEP 1

Assumptions1. The total number of accidents is400. The table provides accurate counts of accidents involving different numbers of vehicles and whether alcohol was involved or not

STEP 2

To answer question15, we need to find the proportion of accidents that involved more than one vehicle. This can be calculated by adding the number of accidents involving2 vehicles and vehicles, and dividing by the total number of accidents.
Proportion of accidents with more than one vehicle=Number of 2 vehicle accidents+Number of  vehicle accidentsTotal number of accidentsProportion\, of\, accidents\, with\, more\, than\, one\, vehicle = \frac{Number\, of\,2\, vehicle\, accidents + Number\, of\,\, vehicle\, accidents}{Total\, number\, of\, accidents}

STEP 3

Plug in the values from the table into the formula.
Proportion of accidents with more than one vehicle=275+50400Proportion\, of\, accidents\, with\, more\, than\, one\, vehicle = \frac{275 +50}{400}

STEP 4

Calculate the proportion of accidents with more than one vehicle.
Proportion of accidents with more than one vehicle=275+50400=325400=0.812Proportion\, of\, accidents\, with\, more\, than\, one\, vehicle = \frac{275 +50}{400} = \frac{325}{400} =0.812So, the answer to question15 is (d) 325400\frac{325}{400} or 81.25%81.25\%.

STEP 5

To answer question16, we need to find the proportion of accidents that involved alcohol and a single vehicle. This can be calculated by dividing the number of such accidents by the total number of accidents.
Proportion of accidents with alcohol and a single vehicle=Number of accidents with alcohol and a single vehicleTotal number of accidentsProportion\, of\, accidents\, with\, alcohol\, and\, a\, single\, vehicle = \frac{Number\, of\, accidents\, with\, alcohol\, and\, a\, single\, vehicle}{Total\, number\, of\, accidents}

STEP 6

Plug in the values from the table into the formula.
Proportion of accidents with alcohol and a single vehicle=50400Proportion\, of\, accidents\, with\, alcohol\, and\, a\, single\, vehicle = \frac{50}{400}

STEP 7

Calculate the proportion of accidents with alcohol and a single vehicle.
Proportion of accidents with alcohol and a single vehicle=50400=0.125Proportion\, of\, accidents\, with\, alcohol\, and\, a\, single\, vehicle = \frac{50}{400} =0.125So, the answer to question16 is (b) 50400\frac{50}{400} or 12.5%12.5\%.

STEP 8

To answer question17, we need to find the proportion of accidents that involved either alcohol or a single vehicle. This can be calculated by adding the number of accidents involving alcohol and the number of accidents involving a single vehicle, subtracting the number of accidents involving both, and dividing by the total number of accidents.
Proportion of accidents with alcohol or a single vehicle=Number of accidents with alcohol+Number of accidents with a single vehicle−Number of accidents with bothTotal number of accidentsProportion\, of\, accidents\, with\, alcohol\, or\, a\, single\, vehicle = \frac{Number\, of\, accidents\, with\, alcohol + Number\, of\, accidents\, with\, a\, single\, vehicle - Number\, of\, accidents\, with\, both}{Total\, number\, of\, accidents}

STEP 9

Plug in the values from the table into the formula.
Proportion of accidents with alcohol or a single vehicle=170+75−50400Proportion\, of\, accidents\, with\, alcohol\, or\, a\, single\, vehicle = \frac{170 +75 -50}{400}

STEP 10

Calculate the proportion of accidents with alcohol or a single vehicle.
Proportion of accidents with alcohol or a single vehicle=170+75−50400=195400=0.4875Proportion\, of\, accidents\, with\, alcohol\, or\, a\, single\, vehicle = \frac{170 +75 -50}{400} = \frac{195}{400} =0.4875So, the answer to question17 is (c) 195400\frac{195}{400} or 48.75%48.75\%.

STEP 11

To answer question18, we need to find the proportion of accidents that involved a single vehicle given that alcohol was involved. This can be calculated by dividing the number of such accidents by the total number of accidents involving alcohol.
Proportion of accidents with a single vehicle given alcohol was involved=Number of accidents with a single vehicle and alcoholTotal number of accidents with alcoholProportion\, of\, accidents\, with\, a\, single\, vehicle\, given\, alcohol\, was\, involved = \frac{Number\, of\, accidents\, with\, a\, single\, vehicle\, and\, alcohol}{Total\, number\, of\, accidents\, with\, alcohol}

STEP 12

Plug in the values from the table into the formula.
Proportion of accidents with a single vehicle given alcohol was involved=50170Proportion\, of\, accidents\, with\, a\, single\, vehicle\, given\, alcohol\, was\, involved = \frac{50}{170}

STEP 13

Calculate the proportion of accidents with a single vehicle given alcohol was involved.
Proportion of accidents with a single vehicle given alcohol was involved=50170=0.294Proportion\, of\, accidents\, with\, a\, single\, vehicle\, given\, alcohol\, was\, involved = \frac{50}{170} =0.294So, the answer to question18 is (b) 50170\frac{50}{170} or 29.41%29.41\%.

STEP 14

To answer question19, we need to find the proportion of accidents that involved alcohol given that multiple vehicles were involved. This can be calculated by dividing the number of such accidents by the total number of accidents involving multiple vehicles.
Proportion of accidents with alcohol given multiple vehicles were involved=Number of accidents with alcohol and multiple vehiclesTotal number of accidents with multiple vehiclesProportion\, of\, accidents\, with\, alcohol\, given\, multiple\, vehicles\, were\, involved = \frac{Number\, of\, accidents\, with\, alcohol\, and\, multiple\, vehicles}{Total\, number\, of\, accidents\, with\, multiple\, vehicles}

STEP 15

Plug in the values from the table into the formula.
Proportion of accidents with alcohol given multiple vehicles were involved=120325Proportion\, of\, accidents\, with\, alcohol\, given\, multiple\, vehicles\, were\, involved = \frac{120}{325}

STEP 16

Calculate the proportion of accidents with alcohol given multiple vehicles were involved.
Proportion of accidents with alcohol given multiple vehicles were involved=120325=0.3692Proportion\, of\, accidents\, with\, alcohol\, given\, multiple\, vehicles\, were\, involved = \frac{120}{325} =0.3692So, the answer to question19 is (c) 120325\frac{120}{325} or 36.92%36.92\%.

STEP 17

To answer question20, we need to find the proportion of accidents that involved alcohol given that3 vehicles were involved. This can be calculated by dividing the number of such accidents by the total number of accidents involving3 vehicles.
Proportion of accidents with alcohol given 3 vehicles were involved=Number of accidents with alcohol and 3 vehiclesTotal number of accidents with 3 vehiclesProportion\, of\, accidents\, with\, alcohol\, given\,3\, vehicles\, were\, involved = \frac{Number\, of\, accidents\, with\, alcohol\, and\,3\, vehicles}{Total\, number\, of\, accidents\, with\,3\, vehicles}

STEP 18

Plug in the values from the table into the formula.
Proportion of accidents with alcohol given 3 vehicles were involved=2050Proportion\, of\, accidents\, with\, alcohol\, given\,3\, vehicles\, were\, involved = \frac{20}{50}

STEP 19

Calculate the proportion of accidents with alcohol given3 vehicles were involved.
Proportion of accidents with alcohol given 3 vehicles were involved=50=.4Proportion\, of\, accidents\, with\, alcohol\, given\,3\, vehicles\, were\, involved = \frac{}{50} =.4So, the answer to question is (b) 50\frac{}{50} or 40%40\%.

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