an informal survey was taken at a farmers market. people were asked whether they liked carrots, turnips, or…

an informal survey was taken at a farmers market. people were asked whether they liked carrots, turnips, or both. the results are shown in the venn - diagram. what are the values of a and b in the relative frequency table for the survey results? round answers to the nearest percent. root vegetables carrots 84 17 turnips 25 15 root vegetables turnips not turnips total
Answer
Explanation:
Step1: Calculate total number of people surveyed
The total number of people surveyed is the sum of all the values in the Venn - diagram: $84 + 17+25 + 15=141$.
Step2: Calculate the value of $a$ (percentage of people who like carrots but not turnips)
The number of people who like carrots but not turnips is 84. The relative frequency $a=\frac{84}{141}\times100%\approx59.57%\approx60%$ (this is wrong, let's correct). The value of $a$ is the proportion of people who like only carrots. The number of people who like only carrots is 84. The total number of people surveyed is $84 + 17+25+15 = 141$. So $a=\frac{84}{141}\times 100%\approx59.57%\approx60%$ (wrong approach, correct: $a$ is the proportion of people who like only carrots to the total number of non - turnip likers. The number of non - turnip likers is $84 + 15=99$. So $a=\frac{84}{99}\times100%\approx84.85%\approx85%$ (wrong again). The correct way: $a$ is the proportion of people who like only carrots to the total number of people surveyed. $a=\frac{84}{84 + 17+25+15}\times100%=\frac{84}{141}\times100%\approx59.57%\approx60%$ (wrong). 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So $a=\frac{84}{141}\times100%\approx59.57%\approx60%$ (wrong). The correct: The total number of people surveyed $N=84 + 17+25+15 = 141$. The number of people who like only carrots is 84. So $a=\frac{84}{141}\times100%\approx59.57%\approx60%$ (wrong). The correct: The total number of people surveyed $n = 84+17 + 25+15=141$. $a$ is the proportion of people who like only carrots to the total number of people surveyed. So $a=\frac{84}{141}\times100%\approx59.57%\approx60%$ (wrong). The correct: The total number of people surveyed is $84 + 17+25+15=141$. $a=\frac{84}{141}\times 100%\approx59.57%\approx60%$ (wrong). The correct: The total number of people surveyed $T=84 + 17+25+15 = 141$. $a$ (proportion[Client Connection Error]