Answer:
The sample size is  [tex]n = 1043 [/tex]
Step-by-step explanation:
From the question we are told that
 The lower bound of the range is a = 51
 The upper bound of the range is b =  710
  The margin of error is [tex]E = 10[/tex]
Generally the standard deviation is mathematically represented as
    [tex]\sigma = \frac{b- a}{4}[/tex]
=> Â Â [tex]\sigma = \frac{710 - 51 }{4}[/tex]
=> Â Â [tex]\sigma = 164.75[/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 Â
  [tex]n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2[/tex]
=> [tex]n = [ 1.96 Â * Â 164.75 }{10} ] ^2[/tex]
=> [tex]n = 1043 [/tex]
