Solutions

Please note that the steps show rounded numbers, but that the final answers to the problems are calculated without rounding.

Problem Part Solution
1 - A pie chart is used for categorical data. Each slice represents a part of a whole. A histogram, on the other hand, is used for quantitative data. It is a visual representation of the spread of a set of data.
2 - pieSurveyData
3 - barSurveyData
4 - paretoSurveyData
5 - The sample proportion \(\hat{p}\) will be approximately normal when \(n\) is large. How do we know if \(n\) is large? We will conclude that \(n\) is large when \(np \geq 10\) and \(n(1 - p) \geq 10\)
6 - n = 100
7 - The sample proportion \(\hat{p}\) will be approximately normal when:
\(np \geq 10\) and \(n(1 - p) \geq 10\)
\(1000(0.528) = 528 \geq 10\) and \(1000(1-0.528) = 472 \geq 10\)
Since both conditions are true, we conclude that \(n\) is sufficiently large so that \(\hat{p}\) will be approximately distributed.
8 - The sampling distribution of \(\hat{p}\) is approximately normal with mean \(p = 0.528\) and \(\text{standard deviation of } 0.016\).
9 - \(z = -1.774\)
10 - \(P(Z=-1.774) = 0.038\)
11 - The sample proportion \(\hat{p}\) will be approximately normal when:
\(np \geq 10\) and \(n(1 - p) \geq 10\)
\(4040(0.5) = 2020 \geq 10\) and \(4040(1-0.5) = 2020 \geq 10\)
Since both conditions are true, we conclude that \(n\) is sufficiently large so that \(\hat{p}\) will be approximately distributed.
12 - The sampling distribution of \(\hat{p}\) is approximately normal with mean \(p = 0.5\) and \(\text{standard deviation of } 0.008\).
13 - \(P(Z=0.881 \text{ or } Z=-0.881) = 0.378\)