document.write( "Question 1010221: For the normally distributed random variables, find the probabilities \r
\n" ); document.write( "\n" ); document.write( "1) P (x-bar > 2.5), if μ = 2.3, σ = 0.8, n = 50 \r
\n" ); document.write( "\n" ); document.write( "2) P (x-bar < 3.1), if μ = 3.0, σ = 1.0, n = 100 \n" ); document.write( "
Algebra.Com's Answer #625714 by mathmate(429)\"\" \"About 
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\n" ); document.write( "Question:
\n" ); document.write( "Find probabilities of the following normally distributed random variables:
\n" ); document.write( "1) P (x-bar > 2.5), given μ = 2.3, σ = 0.8, n = 50
\n" ); document.write( "2) P (x-bar < 3.1), given μ = 3.0, σ = 1.0, n = 100
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "
\n" ); document.write( "Standard deviation of sample mean = σ/sqrt(n)
\n" ); document.write( "Z=(x-μ)/σ
\n" ); document.write( "
\n" ); document.write( "1. S.D. of sample mean = 0.8/sqrt(50) = 0.11314
\n" ); document.write( "P((x-bar) > 2.5)
\n" ); document.write( "=P(Z>(2.5-2.3)/0.13114)
\n" ); document.write( "=P(Z>1.7678)
\n" ); document.write( "=1-P(Z<1.7678)
\n" ); document.write( "=1-0.96145
\n" ); document.write( "=0.03855
\n" ); document.write( "
\n" ); document.write( "2. S.D. of sample mean = 1.0/sqrt(100)=0.10
\n" ); document.write( "P((x-bar)<3.1)
\n" ); document.write( "=P(Z<(3.1-3.0)/0.10)
\n" ); document.write( "=P(Z<1)
\n" ); document.write( "=0.84134
\n" ); document.write( " \n" ); document.write( "
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