Question 1172983
z < (x-mean)/sd/sqrt(n) and z> (-200*sqrt(30)/2400)
z < 200*sqrt(30)/2400
 -0.46 < z < 0.46
probability is 0.3545
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with sample size of 50
it is <abs (200*sqrt(50)/2400 or -0.59 < z < 0.59
probability is 0.4448
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with sample size of 100
it is < abs (200*10/2400) or -0.83 < z < 0.83 
probability is 0.5935
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with n=400 
-1.67 < z < 1.67
probability is 0.9051
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The larger the sample size, the more likely the estimate of the population mean will be within a fixed interval. 
Confidence intervals will be narrower.  The sampling distribution of the sample mean over different sample sizes will become sharper, less variable, the greater the sample size.