document.write( "Question 1201602: APPLES: the annual per capita consumption of fresh apples
\n" ); document.write( "(in pounds) in the united states can be approximated by a normal distribution with a mean of 16.2 pounds and a standard deviation of 4 pounds
\n" ); document.write( "a. what is the smallest annual per capita consumption of apples can be in the top 25% pf consumption?
\n" ); document.write( "b. what is the largest annual per capita consumption of apples that can be in the bottom 15% of consumption? \n" ); document.write( "

Algebra.Com's Answer #836065 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "the annual per capita consumption of fresh apples (in pounds) in the united states
\n" ); document.write( "can be approximated by a normal distribution with a mean of 16.2 pounds
\n" ); document.write( "and a standard deviation of 4 pounds
\n" ); document.write( "(a) what is the smallest annual per capita consumption of apples can be in the top 25% pf consumption?
\n" ); document.write( "(b) what is the largest annual per capita consumption of apples that can be in the bottom 15%
\n" ); document.write( " of consumption?
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\n" ); document.write( "\n" ); document.write( " To solve this problem, forget about apples and concentrate on the given normal curve.\r
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document.write( "Each normal curve is a bell shaped.\r\n" );
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document.write( "In part (a), they want you find the highest raw score z such that the area on the right\r\n" );
document.write( "of this z-score is 0.25 (and, hence, the area on the left of this z-score is 1-0.25 = 0.75).\r\n" );
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document.write( "To find this raw score z, use the function invNorm, which is the inverse function\r\n" );
document.write( "to the cumulative normal distribution function.\r\n" );
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document.write( "This function invNorm is in your calculator TI-83/84.\r\n" );
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document.write( "     Its format is  z = invNorm(area, mean, SD).\r\n" );
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document.write( "In your problem, the input for the calculator function is \r\n" );
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document.write( "    area = 0.75 = 1-0.25; the mean value and SD are given.\r\n" );
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document.write( "So, you print in your calculator invNorm(0.75, 16.2, 4),\r\n" );
document.write( "and you get the answer  z= 18.898 pounds, which you can round to z = 19 pounds.\r\n" );
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document.write( "For instructions on how to get this function invNorm in your calculator, if you need them, \r\n" );
document.write( "see this web-page  https://www.statology.org/invnorm-ti-84/\r\n" );
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document.write( "If you are a beginner student in such calculations, I recommend you to go to web-site\r\n" );
document.write( "https://davidmlane.com/hyperstat/z_table.html.\r\n" );
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document.write( "Find there free of charge online calculator, specially created for such problems.\r\n" );
document.write( "It has perfect design, so any beginner student can work with it on his or her own\r\n" );
document.write( "without help from outside.\r\n" );
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document.write( "    For your problem, use the mode \"value from the area\" \r\n" );
document.write( "    and look for the answer in the window \"Below\".\r\n" );
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document.write( "The calculator will show you the area of interest as shaded, so you will understand\r\n" );
document.write( "everything that you are doing and what the calculator does for you.\r\n" );
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document.write( "This calculator is the best tool for the beginners to learn the subject.\r\n" );
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document.write( "For part (b), the same /(or similar) mantra does work.\r\n" );
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document.write( "In part (b), they want you find the highest raw score z such that the area on the left\r\n" );
document.write( "of this z-score is 0.15.  Notice that this time the area of interest is on the left side\r\n" );
document.write( "of the z-score.\r\n" );
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document.write( "Again, use the standard function invNorm, now in this format\r\n" );
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document.write( "                area  mean  SD    <<<---=== formatting pattern\r\n" );
document.write( "    z = invNorm(0.15, 16.4, 4)\r\n" );
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document.write( "Your answer should be z= 12.054 pounds, which you can round to z= 12 pounds.\r\n" );
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document.write( "For part (b), the same recommendation works regarding the online calculator.\r\n" );
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