University:
Carleton College
Course:
MATH 111 | lntroduction to Calculus
Academic year:

2024
Views:

457

Pages:

3
Author:

Alecai8y

Question 1 How can you use a two-way table to determine probabilities? Answer We would like to explain how we use the two-way table to determine the probability. We determine the probability of any event according to rules and when we need to substitute the value of any category, we should use the exact value of a sample which over by the total number of outcomes or the total number of samples. Question 2 How can you use two way-frequency tables to analyze data? Answer The bi-variate data can be expressed as a two-way frequency table. Two-way frequency table tells the relationship between two variables. For example, two basket ball teams are playig at home and away grounds. The total number of wind for each team both home and away can be calculated and also the home and away win rate can be calculated simultaneously. Baseball teams for the high school and college play at the same stadium. Results are tabulated us Teams Home Away Total WMHS (11,16) (8,14) (19,30 BMC (18,26) (18,30) (36,56) Place WHMS BMC Total Home (11,16) (18,26) (29,42) Away (8,14) (18,30) (26,44) WHMS stands for west mountain high school and BMC stands for big mountain college. The order pair is (win, total matches). Question 3 Here are the row and column totals for a two-way table with two rows and two columns: a b C d 50 50 Find two different sets of counts a, b, c, and d for the body of the table that 60 40 100 give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables. Answer Given: a b 50 C d 50 60 40 100 We then need to find a set of values a, 6,c and d such that row totals are 50 and the column totals are 60 and 40 respectively. This then implies that the following equations need to be satisfied: a+b=50 c+d=50 a+c=60 b+d=40 One possible set of values for a, b, c and d is then a = 30, b = 30, c = 20 and d= 20. 30 30 50 20 20 50 60 40 100 Another possible set of values fora, 8, c and dis then a = 40, b = 10, c = 30 and d = 50. 40 10 50 20 30 50 60 40 100 Question 4 The relative frequencies are the sums of each row and column in a two-way table. (joint, marginal, or conditional) Answer The sums of each row and column in a two-way table are joint probabilities. When the two-way table contains relative frequencies, the sums of each row and column is called the joint relative frequencies. Question 5 In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel. Class First Second Third Survived Yes 197 94 151 No 122 167 476 Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P (not a passenger in first class and survived). Answer Given: Class First Second Third Total Yes 197 94 151 442 Survived No 122 167 476 765 Total 319 261 627 1207 94+151-245 of the 1207 people on the Titanic were not a passenger in first class and survived. The probability is the number of favorable outromes divided by the number of possible outromes: P(FC and D) = #of favorable outromes / #of possible outromes 245 ~ -0.2030 = 20.30% 1207