### 2C Calculate and report the probability that $X$ equals 23 or more, $\\prob(x \\ge 28)$. '{1'} ### ED Create a graph which displays the binomial distribution of $X$ using vertical segments at each value of $X = x$, where the height of the segments indicate the probability $\\prob(x : x}$. For ex \\ge 20$, use a different color for the segments from the rest to help visualize your answer to 2C. Only display values on the plot for $X \\le 56$. - You may use functions from 'ggprob.R', or create the graphic using your own code. If you code from 'ggprob.R', you might elect to use 'gbinom(}' with argument 'b=56' to plot the probabilities from G to 50 in one color and then add a layer using 'geom_binom_density()' to overlay line segments in a different color by 'color 2 "somecolorname"' and "a = 20' as arguments. The arguments "a" and 'b' are the left and right arguments for the range of probabilities to graph in 'gbinom{)' and 'geom_binom_density()'. when not specified, the code extends the missing endpoint(s} to the edge of the plotting area. The values of "n" and 'p' need to be set in each layer: they are not aesthetics mapped to variables within 'aes{]" that are inherited by subsequent layers. '{T} ### 3 what is the probability that $X$ from Problem 2 is within one, two, and three standard deviations of the mean? Round each probability to four decimal places. '{T} ### 4 Draw a graph of the binomial distribution from Problems 2 and 3 and add vertical lines at the mean {solid} and 1, 2, and 3 standard deviations above and below the mean (dashed). Use code from 'ggprob.R', or create the graphic using your own code. Unly display values for X between G and 4B