Describing Shape of Histogram with Smooth Curve

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Questions and Answers

What is the value of the standard deviation of the data variable 'abssim'?

  • 161.8665
  • 0.0004195217
  • 7.610036 (correct)
  • 189

Which curve is well known for approximating many natural phenomena and can model data resulting from combining a large number of independent variables?

  • The Logarithmic Curve
  • The Exponential Curve
  • The Sine Curve
  • The Normal Curve (correct)

What are the two parameters of the Normal probability density function (pdf)?

  • Range and interquartile range
  • Population mean and population SD (correct)
  • Standard error and mode
  • Median and quartile deviation

What does the cumulative distribution function (CDF) represent in the context of the Normal curve?

<p>Area under the curve up to a point (D)</p> Signup and view all the answers

If we draw a smooth curve as an approximation of the histogram based on the data provided, what would be a key characteristic of this curve?

<p>It follows a Normal distribution (A)</p> Signup and view all the answers

What does the length(data$abssim[data$abssim > 189])/length(data$abssim) ratio indicate?

<p>Percentage of values above 189 in 'abssim' (B)</p> Signup and view all the answers

Based on the code provided, what is the mean height of the students?

<p>163.6204 (B)</p> Signup and view all the answers

What does the standard deviation value of 7.657661 represent?

<p>Measure of the spread of student heights (C)</p> Signup and view all the answers

In the context provided, what proportion of women fall in the height category 160-165?

<p>0.286 (D)</p> Signup and view all the answers

What is the purpose of simulating data using proportions in a table?

<p>To represent real-world data (A)</p> Signup and view all the answers

In the given code snippet for plotting a histogram, what does 'geom_histogram' do?

<p>Plots a bar chart (B)</p> Signup and view all the answers

How many women in the simulated data could fall under the height category of 175-180?

<p>0.029 (C)</p> Signup and view all the answers

What does the area under a histogram represent up to a point x?

<p>The chance of getting data up to that point (D)</p> Signup and view all the answers

When a variable X is Normally distributed with mean μ and standard deviation σ, how is it denoted?

<p>X ~ N(μ, σ) (B)</p> Signup and view all the answers

What does the '68%-95%-99.7% Rule' state about Normal curves?

<p>All of the above (D)</p> Signup and view all the answers

In Normal distribution, what are standard units (z-scores)?

<p>How many standard deviations a point is from the mean (A)</p> Signup and view all the answers

For a model X ~ N(161.9, 7.62), what does 161.9 represent?

<p>Mean (B)</p> Signup and view all the answers

If a variable follows the distribution of a Normal curve, what can be used as an approximation to the area under a histogram?

<p>$P(X &gt; x)$ (A)</p> Signup and view all the answers

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