A random sample of size n = 178 is taken from a population of size N = 3,718 with mean μ = −80 and variance σ 2 = 190. [You may find it useful to reference the z table .] a-1. Is it necessary to apply...

A random sample of sizen = 178 is taken from a population of sizeN = 3,718 with meanμ = −80 and varianceσ
² = 190.[You may find it useful to reference thez table.]

a-1.Is it necessary to apply the finite population correction factor?

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  Yes

  
  

  
  
  
  


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  No

  
  

  
  
  
  

a-2.Calculate the expected value and the standard error of the sample mean.(Negative values should be indicated by a minus sign. Round "standard error" to 2
decimal places.)

b.What is the probability that the sample mean is between −82 and −78?(Round “z” value to 2 decimal places, and final answer to 4 decimal places.)