Question

The average number of words in a romance novel is 64,141 and the standard deviation is 17,010. 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.a. What is the distribution of X? X ~ Nb. Find the proportion of all novels that are between 70,945 and 81,151 words.c. The 85th percentile for novels iswords. (Round to the nearest word)d. The middle 40% of romance novels have fromwords to words. (Round to the nearest word)

Answer 1

Part A

What is the distribution of X?

The notation is N ( μ, σ )

so

N (64,141 , 17,010)

Part B

Find the proportion of all novels that are between 70,945 and 81,151 words

Remember that

z =(x - μ)/σ

where

μ=64,141 words

σ=17,010 words

For x=70,945 -------> Z=(70,945-64,141)/17,010 ---------> Z=0.4

For x=81,151 ---------> Z=(81,151-64,141)/17,010 --------> Z=1

using a z-score table values

P=0.1859

Part C

The 85th percentile for novels is?

Remember that

If your score is in the 85th percentile, it means that 85% of the scores are below your score and 15% are above your score

using a z-score table values

Z = 1.036

Find out the value of X

1.036=(x-64,141)/17,010

X=81,763 words

Part D

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