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
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[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]
=> [tex]n = [1.96 * 3750 }{200} ] ^2[/tex]
=> [tex]n =1351 [/tex]
