Question 445391
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Hi
september energy consumption levels for a single-family homes are found to be normally distributed
{{{mu}}} of 1030kwph and a {{{sigma}}}of 22kwh
probability that for 16 randomly selected homes, 
the average energy consumption in September is less than 1021kWh
  *Note: {{{z = (x - mu)/((sigma)/sqrt(n))}}}
    z = {{{ (1021-1030)/(22/4) = -9/(22/4) = -9/5.5 = -1.6364}}}
   P( z < -1.6364) = .0509        NORMSDIST(-1.6364)per Excel

Point being not much probability of that happening
{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)), green(line( -1.6364,0, -1.6364,exp(-1.6364^2/2))),locate(4.8,-.01,z),locate(4.8,.2,z))}}}