document.write( "Question 1191027: A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 80 thousand miles and a standard deviation of 12 thousand miles. \r
\n" ); document.write( "\n" ); document.write( "How many miles will be traveled by at least ​70% of the​ trucks? \n" ); document.write( "
Algebra.Com's Answer #822832 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the mean is 80,000 and the standard deviation is 12,000.
\n" ); document.write( "the z-score for the probability that at least 70% of the trucks travel is equal to .5244.
\n" ); document.write( "the z-score formula is z = (x - m) / s
\n" ); document.write( "z = .5244
\n" ); document.write( "x = what you want to find.
\n" ); document.write( "m = mean = 80,000
\n" ); document.write( "s = standard deviation = 12,000
\n" ); document.write( "formula becomes:
\n" ); document.write( ".5244 = (x - 80,000) / 12,000.
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = .5244 * 12,000 + 80,000 = 86,292.8
\n" ); document.write( "replac4e x with that in the formula and you should get the z-score of .5244.
\n" ); document.write( "z = (86,292.8 - 80,000) / 12,000 = .5244.
\n" ); document.write( "find the area to the left of that z-score and you should get something very close to .7.
\n" ); document.write( "i got .6999998412.
\n" ); document.write( "you won't get .7 right on because .5244 is a rounded number.
\n" ); document.write( "the actual z-score that i got, using the ti-84 plus, was .5244005102.
\n" ); document.write( "in order to get a z-score of .5244 from the z-score tables, i had to do a manual interpolation.
\n" ); document.write( "the full z-score value from that was .5244092219.
\n" ); document.write( "i rounded to .5244.
\n" ); document.write( "the table only shows you the z-score rounded to 2 decimal digits.
\n" ); document.write( "what i got manually was actually better than that.
\n" ); document.write( "an online calculator i used, got me a z-score of .524.
\n" ); document.write( "if you rounded your z-score to what the table was s howing you, you would have gotten a z-score of .52.
\n" ); document.write( "that's because:
\n" ); document.write( "z-score of .52 gives you an area of .69847 to the left of it.
\n" ); document.write( "z-score of .53 gives you an area of .70194 to the left of it.
\n" ); document.write( ".70000 - .69847 = .00153.
\n" ); document.write( ".70194 - .70000 = .00194.
\n" ); document.write( "z-score of .52 gives you an area that is closer to .70000, so you would pick that.\r
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\n" ); document.write( "\n" ); document.write( "here's the table i used.
\n" ); document.write( "https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf\r
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\n" ); document.write( "\n" ); document.write( "if you used the z-score of .52 from the table, you would have gotten a raw score of x = .52 * 12,000 + 80,000 = 86240.
\n" ); document.write( "i got 86,292.8 when rounding the z-score to 4 decimal digits.
\n" ); document.write( "the result are close, but different.
\n" ); document.write( "it depend on what your instructor expects when you solve for this.\r
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\n" ); document.write( "\n" ); document.write( "if i used the calculator and didn't do any rounding, i would have gotten 86292.80612.
\n" ); document.write( "rounding to 4 decimal digits was definitely closer then rounding to 2.\r
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\n" ); document.write( "\n" ); document.write( "let me know if you have any questions or concerns.
\n" ); document.write( "theo\r
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