Answer:
The value is  [tex]n =1351 [/tex]
Step-by-step explanation:
From the question we are told that
 The standard deviation is  [tex]\sigma = \$3750[/tex]
  The margin of error is  [tex]E = \$ 200[/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 sample size is mathematically represented as
     [tex]n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2[/tex]
=> Â Â Â [tex]n = [1.96 Â * Â 3750 }{200} ] ^2[/tex]
=> Â Â Â [tex]n =1351 [/tex]
