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

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]