The average number of words in a romance novel is 64,289 and the standard deviation is 17,272. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible. b. Find the proportion of all novels that are between 62,562 and 79,834 words. ________________ c. The 85th percentile for novels is words. (Round to the nearest word) ________________ d. The middle 70% of romance novels have from _______ words to _______ words. (Round to the nearest word)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The average number of words in a romance novel is 64,289 and the standard deviation is 17,272. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.
b. Find the proportion of all novels that are between 62,562 and 79,834 words. ________________
c. The 85th percentile for novels is words. (Round to the nearest word) ________________
d. The middle 70% of romance novels have from _______ words to _______ words. (Round to the nearest word)
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