Question

The mean per capita income is 15,654 dollars per annum with a standard deviation of 570

dollars per annum.

What is the probability that the sample mean would differ from the true mean by less than  63 dollars if a sample of 315 persons is randomly selected? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 15654

standard deviation = = 570

n = 315

= = 15654

= / n = 570 / 315 = 32.1159

P( 15591 < < 15717) = P((15591 - 15654) /32.1159 <( - ) / < (15717 - 15654) / 32.1159))

= P(-1.96 < Z < 1.96)

= P(Z < 1.96) - P(Z < -1.96) Using standard normal table,  

= 0.9750 - 0.025

= 0.9500

The probability that the sample mean would differ from the true mean by less than  63 dollars if a sample of 315 persons is randomly selected is 0.9500