Suppose that Felisha is a librarian, and she can read in a scholarly journal that the number of words in a children's picture books published since 1950 is normally distributed with a mean of 802.2 words and a standard deviation of 112.0 words. She wishes to construct a confidence interval for the mean number of words in all children's picture books after 2010, in case the number has changed in fencer years. Felisha took a random sample of 20 children's picture books published after 2010 and counted the number of words in all 20 books. Her data is presented in a stem leaf plot.
49, 51, 59, 60, 64, 65, 70, 73, 74, 76, 78, 81, 83, 84, 86, 91, 95, 99, 101, 107
Leaf unit = 10
Felisha calculated the mean of her sample to be 773.0 words, and now she wants to calculate the margin of error of a 90% confidence interval for the mean number of words in all books published after 2010. She assumes that the number of words in a children's picture book published after 2010 has the same normal distribution and same standard deviation as the general population of all books published since 1950.
Compute the margin of error of a 90% confidence interval for the mean number of words in all children's books Published after 2010. Give your answer to one decimal place.