document.write( "Question 1077769: 8.1 #5
\n" ); document.write( "A simple random sample of size n=12 is obtained from a population with
\n" ); document.write( "μ=69 and σ=16.
\n" ); document.write( "=
\n" ); document.write( "(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample​ mean? Assuming that this condition is​ true, describe the sampling distribution of
\n" ); document.write( "x ( with overbar on top of x).
\n" ); document.write( "​(b) Assuming the normal model can be​ used, determine ​P(x<72.2​).
\n" ); document.write( "​(c) Assuming the normal model can be​ used, determine ​P(x≥70.7​).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I know what A is, μx=69 and σ=16/the square root of 16\r
\n" ); document.write( "\n" ); document.write( "I just don't know what b or c are. thank you!\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #692294 by Boreal(15235)\"\" \"About 
You can put this solution on YOUR website!
z=(72.2-69)/(16/sqrt(12))--not sqrt (16)
\n" ); document.write( "=0.6928
\n" ); document.write( "probability < 0.6928 is 0.7558.
\n" ); document.write( "probability x > 70.7 is z > (1.7)/16/sqrt(12)=0.3680
\n" ); document.write( "That probability is 0.3564 \n" ); document.write( "
\n" );