document.write( "Question 1170283: CNNBC recently reported that the mean annual cost of auto insurance is 1034 dollars. Assume the standard deviation is 224 dollars. You take a simple random sample of 83 auto insurance policies.\r
\n" ); document.write( "\n" ); document.write( "Find the probability that a single randomly selected value is less than 998 dollars.
\n" ); document.write( "P(X < 998) = \r
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\n" ); document.write( "\n" ); document.write( "Find the probability that a sample of size
\n" ); document.write( "n
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\n" ); document.write( "83
\n" ); document.write( " is randomly selected with a mean less than 998 dollars.
\n" ); document.write( "P(M < 998) = \r
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\n" ); document.write( "\n" ); document.write( "Enter your answers as numbers accurate to 4 decimal places \n" ); document.write( "

Algebra.Com's Answer #795246 by Boreal(15235) $\"\"$ $\"About$

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z=(x-mean)/sd=-36/224
\n" ); document.write( "that probability off z < that value is 0.4362
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\n" ); document.write( "z=(x-mean)/sigma/sqrt(n), assuming the sd is known for the population, which it likely is here.
\n" ); document.write( "z < (998-1034)/224/sqrt(83)
\n" ); document.write( "=-36*sqrt(83)/224=-1.464\r
\n" ); document.write( "\n" ); document.write( "that probability is 0.0716.
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