Create a program in R using vectorized calculation. No use of loops is needed. Make a data frame consisting of 20 and 10 columns. Each column j should consist of 20 values from a normal distribution...

Create a program in R using vectorized calculation. No use of loops is needed. Make a data frame consisting of 20 and 10 columns. Each
column j should consist of 20 values from a normal distribution with mean (j-1) and standard deviation 0.5j. For example, the third column should be normal(mean=2, sd=1.5). Using this data frame, do each of the following (using code, of course):

a. Find the mean and standard deviation for each column.
b. Write code that counts the number of columns for which the sample mean and sample
standard deviation are within 20% of the values used to generate the data.
c. Write code that writes the columns from part b to a new data frame.
d. For each value in the new data frame, subtract its column mean and divide by the
column standard deviation.