Suppose that Felisha is a librarian, and she read in a scholarly journal that th

Question

Suppose that Felisha is a librarian, and she read in a scholarly journal that the number of words in children's picture books published since 1950 is normally distributed with a mean of 802.2 words and a standard deviation of 75.0 words. She wishcs to construct a confidence interval for the mean number of words in all children's picture books published after 2010, in case the number has changed in recent 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 the stem-and-leaf plot PlorPublie 201) 7 0 3 4 6 8 10 1 7 Leaf Unit 10 Scroll Felisha calculated the mean of her sample to be 773.0 words, and now she wants to calculate the margin of error of 99% confidence interval for the mean number of words in all books published after 2010. She assumes that the number of words in bunf

Explanation / Answer

The standard deviation of number of words = 75

Number of samples = 20

Standard error of sampling distribution of mean number of words = SD / sqrt(n) = 75 / sqrt(20) = 16.77

Z value for 99% confidence interval is 2.58

Margin of error = Z * Standard error

= 2.58 * 16.77 = 43.2 words

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