Answer:
The 95% confidence interval  is  [tex] 17.932  <  \mu <  20  + 22.068[/tex]
Step-by-step explanation:
From the question we are told that
 The population standard deviation is  [tex]\sigma =7 \ inches[/tex]
 The sample size is  n  =  20
 The sample mean is  [tex]\= x = 20[/tex]
From the question we are told the confidence level is  95% , hence the level of significance is  Â
   [tex]\alpha = (100 - 95 ) \%[/tex]
=> Â [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is Â
  [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]
Generally the margin of error is mathematically represented as Â
   [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]
=> Â Â [tex]E = 1.96 * Â \frac{7 }{\sqrt{20} }[/tex]
=> Â Â [tex]E = 2.068[/tex] Â Â Â Â
Generally 95% confidence interval is mathematically represented as Â
   [tex]\= x -E <  \mu <  \=x  +E[/tex]
=> Â Â [tex] 20 Â - 2.068 Â < Â \mu < Â 20 Â + 2.068[/tex]
=> Â Â [tex] 17.932 Â < Â \mu < Â 20 Â + 22.068[/tex]
