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Answer to Question #202055 in Statistics and Probability for kim
Question #202055
The average number of pages in a novel is 326 with a standard deviation of 24
pages. If a sample of 50 novels is randomly chosen, what is the probability that
the average number of pages in these books is between 319 and 331?
Expert's answer
"\\mu=326 \\\\\n\n\\sigma=24 \\\\\n\nn=50 \\\\\n\nP(319< \\bar{X}<331) = P(\\bar{X}<331) -P(\\bar{X}<319) \\\\\n\n= P(Z <\\frac{331-326}{24\/ \\sqrt{50}}) -P(Z< \\frac{319-326}{24 \/ \\sqrt{50}}) \\\\\n\n= P(Z< 1.473) -P(Z< -2.062) \\\\\n\n= 0.9296 -0.0196 \\\\\n\n= 0.91"
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