Answer:
The number of people needed  is [tex]n =684[/tex] Â
Step-by-step explanation:
From the question we are told that
 The population proportion is  [tex]p = 0.65[/tex]
  The margin of error is  [tex]E = 0.03[/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
    [tex]n =[ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * p(1-p)[/tex]
=> Â Â [tex]n =[ \frac{1.645 }{0.03} ]^2 * 0.65(1-0.65)[/tex]
=> Â Â [tex]n =684[/tex] Â
