### 5 The following code makes a graph of the cumulative distribution function for the binomial distribution, that is $F(x) = \\prob(X \\le x)$ for $X \\sim \\text{Binomial} (7, 0.3)$. This is the function which is calculated by the base R function pbinom( ) " . ### 5A Modify the code to add a horizontal red dotted line at 0.4. "{r } prob5 = tibble( x = seq( -1, 8, 1) , p = dbinom(x, 7, 0.3), cdf = pbinom(x, 7, 0.3) ) ggplot (prob5, aes(x = x, y = cdf ) ) + geom_step (color = "blue" ) + geom_hline (yintercept = 0) + scale_x_continuous (breaks = 0:7) + xlab("x") + ylab ("Probability") + ggtitle( "Binomial(7, 0.3) distribution CDF") + theme_minimal( ) ### 5B Calculate the 0.4 quantile of this distribution. ### 5C Explain how the value of the quantile is related to the red dotted line which you added to the plot. > [Write your answer here] ### 5D Use the graph to determine the 0.75 quantile of this distribution. Then verify your observation with a calculation. {r} ### 6 After this assignment is due the Green Bay Packers will have ten more regular season games to play