Question

5 The city of Decima, Texas has 8,000 registered voters whose average annual income is $36,000 with a population standard deviation of $3600.  If you were to take a sample of 100 registered voters, what is the probability the sample mean ,would be within plus or minus $500 of the population mean?

Answer 1

Solution :

Given that ,

mean = = 36000

standard deviation = = 3600

n = 100

=   = 36000

= / n = 3600 / 100 = 360

P(35500 < < 36500)  

= P[(35500 - 36000) / 360 < ( - ) / < (36500 - 36000) / 360 )]

= P(-1.39 < Z < 1.39 )

= P(Z < 1.39) - P(Z < -1.39 )

Using z table,  

= 0.9177 - 0.0823

= 0.8354