The data: $a_{11} = 8$, $a_{12} = 9$, $a_{13} = 12$, $a_{21} = 160$, $a_{22} = 44$, $a_{23} = 235$ which is represented in the following table, were derived from a study of the effectiveness of a flu vaccine. The value in each cell of the table represents the number of individuals in that category. Some participants in the study were given no vaccine, some were given one injection, and some were given two injections. egin{tabular}{|l|c|c|c|} hline & No Vaccine & One Injection & Two Injections \ hline Flu & 8 & 9 & 12 \ No Flu & 160 & 44 & 235 \ hline end{tabular} What is the probability that a person received two injections? Note: For any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places.
Added by Lisa S.
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Step 1: Calculate the total number of individuals who received two injections by adding the values in the "Two Injections" category: 235 + 12 = 247. Show moreā¦
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A study of the effectiveness of a flu vaccine was conducted with a sample of 500 people. Some participants in the study were given no vaccine, some were given one injection, and some were given two injections. The results of the study are given in the table. $$ \begin{array}{|l|r|r|r|} & \text { Flu } & \text { No flu } & \text { Total } \\ \hline \text { No vaccine } & 7 & 149 & 156 \\ \text { One injection } & 2 & 52 & 54 \\ \text { Two injections } & 13 & 277 & 290 \\ \text { Total } & 22 & 478 & 500 \\ \hline \end{array} $$ A person is selected at random from the sample. Find each probability. (a) The person had two injections. (b) The person did not get the flu. (c) The person got the flu and had one injection.
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The data gathered from a survey of a random group of undergraduate university students about their academic standing are: a11 =148 , a12 =72 , a13 =112 , a14 =95 , a21 =1,332 , a22 = 703 , a23 =980 , a24 =820 , a31 =543 , a32 =328 , a33 =98 , a34 =64 The following contingency table was created based on the above data, where you will need to calculate the grand total, the total for each row, and the total for each column on your own before answering the question that appears after the table. Academic Standing Freshman Sophomore Junior Senior Total Honors 148 72 112 95 Satisfactory 1,332 703 980 820 Probation 543 328 98 64 Total What is the probability of a student having a "Satisfactory" academic standing, given that the student is a senior? (For answers up to four decimal places, enter the number in the box below without rounding it. For answers that have more than four decimal values, round your answer to four decimal places).
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