Question
The average number of words in a romance novel is 64,182 and the standard deviation is 17,154 A. Find the proportion of all novels that are between 50,000 and 60,000 words. square disappointed B. The 90^th percentile for novels is [Select] square words. C. On a shelf with 350 novels, how many would be estimated to have more than 70,000 words? square
Answer
4.3
(148 Votes)
Imogen
Veteran · Tutor for 10 years
Answer
A. 0.1607 B. 88,770 wordsC. 44 novels
Explanation
This question involves understanding the usage and application of mathematical statistics, mainly knowledge of means, standard deviations, percentiles, and ideas relating to normal distribution. A. Given that the mean (average number of words) is 64,182 and the standard deviation is 17,154, z-scores are to be calculated next to find the proportion of novels with a word count between 50,000 and 60,000. The formula for a z score ("value - mean/standard deviation") gives values corresponding to 50,000 and 60,000 under the normal curve.B. The 90th percentile is equivalent to the Ogive percentage. We use that percentage value in the standard normal cumulative distribution function for the z-variable. Then we revert the z-variable for the cumulative(Q) back into x which represents original percentile in term of the word's amount (x=σz+µ).C. With a mean of 64,182 and a standard deviation of 17,154, developing a z-score with a value of 70,000 can return a probability. Multiplying this probability by 350 gives the estimated number of novels likely to contain more than 70,000 words.