SOLUTION: Hi, I'm stuck with this question, please help me :( An economist wishes to estimate the average family income in a certain population. The population standard deviation is known t

Algebra ->  Probability-and-statistics -> SOLUTION: Hi, I'm stuck with this question, please help me :( An economist wishes to estimate the average family income in a certain population. The population standard deviation is known t      Log On


   

Question 446013: Hi, I'm stuck with this question, please help me :(
An economist wishes to estimate the average family income in a certain population. The population standard deviation is known to be $4,500 ; and the economist uses a random sample of size n=225. What is the probability that the sample mean will fall within $800 of the population mean?
Thanks you !
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

*Note: z+=blue+%28x+-+mu%29%2Fblue%28sigma%2Fsqrt%28n%29%29

 %28x+-mu%29+ = 800 , n = 225 and sigma+=+4500

    z = 800/4500/15 =  800/300 = 2.6667  P(z < 2.6667 = .9962

And z = -800/300 = -2.6667  P(z < -2.667) = .0038

 P( -2.667 > z < 2.6667) = .9962-.0038 = .9924