Answer:
0.4246
Step-by-step explanation:
Given data:
mean (<em> u</em> ) = 15 inches
std ( б )= 6 inches
sample size( n ) = 46
<em>u</em>x = mean sample length
Determine the probability that x within 0.5 inch of the claimed population mean
<em>u</em>x = <em>u = </em>15
бx = б/ √ 46 = 6 /√ 46 = 6 / 6.78 = 0.88
Hence the P( 14.5 < x < 15.5 )
= P ( [14.5 - 15 / 0.88 ] < z < (15.5 - 15) / 0.88) )
= P ( -0.5682 < z < 0.5682 )
= P ( z < 0.5682 ) - P ( z < -0.5682 )
= 0.7123 - 0.2877 ( from Z table )
= 0.4246