document.write( "Question 665313: The grades on certain statistics tests are normally distributed with a mean of 76 and a standard deviation of 8. Find the probability that a randomly chosen score from this test is less than or equal to 72.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #413809 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Hi, there--\r\n" );
document.write( "\r\n" );
document.write( "Problem:\r\n" );
document.write( "The grades on certain statistics tests are normally distributed with a mean of 76 and a \r\n" );
document.write( "standard deviation of 8. Find the probability that a randomly chosen score from this test is \r\n" );
document.write( "less than or equal to 72.\r\n" );
document.write( "\r\n" );
document.write( "Solution:\r\n" );
document.write( "First, we find the z-score which allows us to compare this normal curve with the standard \r\n" );
document.write( "normal curve. We have\r\n" );
document.write( "mean = μ = 76\r\n" );
document.write( "standard deviation = σ=8\r\n" );
document.write( "randomly chosen score = x = 72\r\n" );
document.write( "\r\n" );
document.write( "We want to know P (x≤72).\r\n" );
document.write( "\r\n" );
document.write( "z = (x -μ)/σ = (72-76)/8 = -0.5\r\n" );
document.write( "\r\n" );
document.write( "Most z-tables will have a shaded picture of a normal curve which tells you how to interpret \r\n" );
document.write( "the z-vales,\r\n" );
document.write( "\r\n" );
document.write( "P (x≤72) = P(z≤-0.5) = 0.3085\r\n" );
document.write( "\r\n" );
document.write( "The probability of getting a score less than or equal to 76 is 0.3085.\r\n" );
document.write( "\r\n" );
document.write( "~Mrs.Figgy\r\n" );
document.write( "
\n" ); document.write( "
\n" );