Answer:
The sample  size is  [tex]n =68[/tex]
Step-by-step explanation:
  The population proportion is  [tex]\^ p = 0.50[/tex]
   The margin of error is  [tex]E = 0.1[/tex]
From the question we are told the confidence level is  90% , hence the level of significance is  Â
   [tex]\alpha = (100 - 90 ) \%[/tex]
=> Â [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is Â
  [tex]Z_{\frac{\alpha }{2} } =  1.645 [/tex]
Generally the sample size is mathematically represented as Â
  [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> Â [tex]n = [\frac{1.645 }{0.1} ]^2 * 0.50 Â (1 - 0.50 ) [/tex]
=> Â [tex]n =68[/tex]
  Â
