document.write( "Question 1023575: By the empirical rule, what percentage of the area under the normal curve lies between mu - 3sd and mu + 3sd? Put your answer as a percentage.Is the z value, positive or negative? \n" ); document.write( "
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\n" ); document.write( "Question: (edited)
\n" ); document.write( "By the empirical rule, what percentage of the area under the normal curve lies between μ-3σ and μ+3σ? Put your answer as a percentage.Is the z value, positive or negative?
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\n" ); document.write( "Solution:
\n" ); document.write( "A. area between μ-3σ and μ+3σ
\n" ); document.write( "Use a normal distribution table, calculator or a software to find
\n" ); document.write( "P(Z<=μ-3σ)=0.0013499
\n" ); document.write( "P(Z<=μ+3σ)=0.9986501
\n" ); document.write( "and therefore
\n" ); document.write( "area = P(Z<=μ+3σ)- P(Z<=μ-3σ)
\n" ); document.write( "=0.9973002
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\n" ); document.write( "B. Answer in percentage
\n" ); document.write( "Multiply the answer in (A) by 100% to get answer as a percentage.
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\n" ); document.write( "C. The sign of values of Z
\n" ); document.write( "Z is calculated by
\n" ); document.write( "Z=(X-μ)/σ.
\n" ); document.write( "When X=μ, then Z=0.
\n" ); document.write( "Similarly, when X<μ Z is negative, while when X>μ Z is positive.
\n" ); document.write( "σ is always positive, since it is the square-root of the variance.
\n" ); document.write( "Look at the given expressions to determine if the Z-values are positive or negative. \n" ); document.write( "
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