Question

If the population parameter is $400, with a standard deviation of $100. What percentage of your potential sample statistics from the population of size 1,000 will fall between a value of $393.68 and $406.32?

Answer 1

We have,

Upper limit of interval = 406.32

Margin of error = 406.32 - 400 = 6.32

Now, Margin of error = Z_alpha/2 * ( SD / n^0.5 )

6.32 = Z_alpha/2 * ( 100 / 1000^0.5 )

Z_alpha/2 = 2

Using standard normal tables we find the percentage corresponding to 2

alpha / 2 = 0.02283

Alpha = 0.04566

Percentage of your potential sample statistics from the population of size 1,000 will fall between a value of $393.68 and $406.32 = 1 - Alpha = 1 - 0.04566 = 0.9543 = 95.43 % = 95 % ( Approximately)