R 如何对落在数字范围内的变量进行分组

我是这样的一个DF

my_df <- data.frame(
    b1 = c(2, 6, 3, 6, 4, 2, 1, 9, NA), 
    b2 = c(100, 4, 106, 102, 6, 6, 1, 1, 7), 
    b3 = c(75, 79, 8, 0, 2, 3, 9, 5, 80), 
    b4 = c(NA, 6, NA, 10, 12, 8, 3, 6, 2),
    b5 = c(2, 12, 1, 7, 8, 5, 5, 6, NA),
    b6 = c(9, 2, 4, 6, 7, 6, 6, 7, 9),
    b7 = c(1, 3, 7, 7, 4, 2, 2, 9, 5),
    b8 = c(NA, 8, 4, 5, 1, 4, 1, 3, 6),
    b9 = c(4, 5, 7, 9, 5, 1, 1, 2, 12))

我想基于以下假设创建一个新专栏(New).

如果b9=2，则写入黄色. 如果b9介于4和7之间，则写为白色. 如果b9为&gt；=9，则写入绿色

我们的 idea 是创造出这样的东西.

my_df1 <- data.frame(
        b1 = c(2, 6, 3, 6, 4, 2, 1, 9, NA), 
        b2 = c(100, 4, 106, 102, 6, 6, 1, 1, 7), 
        b3 = c(75, 79, 8, 0, 2, 3, 9, 5, 80), 
        b4 = c(NA, 6, NA, 10, 12, 8, 3, 6, 2),
        b5 = c(2, 12, 1, 7, 8, 5, 5, 6, NA),
        b6 = c(9, 2, 4, 6, 7, 6, 6, 7, 9),
        b7 = c(1, 3, 7, 7, 4, 2, 2, 9, 5),
        b8 = c(NA, 8, 4, 5, 1, 4, 1, 3, 6),
        b9 = c(4, 5, 7, 9, 5, 1, 1, 2, 12),
        NEW = c("white", "white", "white", "green", "white", "yellow", "yellow", "yellow", "green"))

我以为这样的事情就能解决问题，但事实并非如此.

greater_threshold <- 2
greater_threshold1 <- 4
greater_threshold2 <- 7
greater_threshold3 <- 9

my_df1 <- my_df %>%
    mutate(NEW = case_when(b9 <= greater_threshold ~ "yellow", b9 >= greater_threshold1 | b9 <= greater_threshold2 ~ "white", b9 >= greater_threshold3 ~ "green"))
                       

任何帮助都将不胜感激.