View the following FOUR lines of code.

library(tidyverse) # End of line 1
data

Question

View the following FOUR lines of code.

library(tidyverse) # End of line 1
data <- data.frame(x = c(rnorm(100, 25, 3) , rnorm(100, 5, 3))) # End of line 2
ggplot(data, aes(x = x)) + geom_histogram(bins = 14) + # End of line 3
labs(x = "Avg. Daily Temperature", y = "Days with that temperature") # End of line 4

In which line of code is the Normal curve plotted?

BlackTom AI · Accepted Answer

No Normal curve is plotted because none of the four lines add a density or a function layer (e.g., geom_density or stat_function) to the ggplot.

1) Relevant knowledge points and concepts
- ggplot layers: geom_histogram draws bars; geom_density or stat_function are required to draw a smooth density or a theoretical curve. 
- labs only sets axis labels. 
- Creating a data frame or loading packages does not by itself add plotting layers.
- To overlay a theoretical normal curve on a histogram you must scale the histogram to density (aes(y = ..density..)) and add stat_function(fun = dnorm, args = list(mean=..., sd=...)) or geom_density.

2) Step-by-step reasoning through the code lines
- Line 1: library(tidyverse) — loads packages. No plot produced.
- Line 2: data <- data.frame(x = c(rnorm(100, 25, 3), rnorm(100, 5, 3))) — generates 200 observations (100 from N(25,3) and 100 from N(5,3)) and stores them. This creates data but does not draw any curve.
- Line 3: ggplot(data, aes(x = x)) + geom_histogram(bins = 14) + — adds a histogram layer with 14 bins. A histogram is a bar chart of counts (or densities), not a normal curve. No density overlay function is called here.
- Line 4: labs(x = "Avg. Daily Temperature", y = "Days with that temperature") — only labels axes.

3) Intermediate calculations (describe the data distribution)
- Combined mean = (100*25 + 100*5) / 200 = (2500 + 500)/200 = 3000/200 = 15.
- Component variances = 3^2 = 9. Compute overall variance:
  average of (var + mean^2) = ((9 + 25^2) + (9 + 5^2)) / 2 = (9+625 + 9+25)/2 = (634 + 34)/2 = 668/2 = 334.
  overall variance = 334 - (overall mean)^2 = 334 - 15^2 = 334 - 225 = 109.
  overall sd ≈ sqrt(109) ≈ 10.44.
(These show what a fitted normal would use, but no such fit is plotted in the code.)

4) Why the correct answer is correct
None of the lines call geom_density, stat_function, or otherwise add a normal curve. The code only loads tidyverse, creates data, draws a histogram, and sets labels.

5) Why other options (lines 1–4) are incorrect
- Line 1: only loads packages.
- Line 2: creates the sample data, does not plot.
- Line 3: draws a histogram (bars), not a normal curve.
- Line 4: sets axis labels only.

6) Conclusion
Therefore the correct choice is "None of the answers given." This matches the provided answer.

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