A random sample of 25 students is taken out of 1000 students

A random sample of 25 students is taken out of 1,000 students taking the GMAT exam. The mean test score for the Sample is 480 and the standard deviation for the entire population of 500 students is 30. Find the 95% confidence interval for the unknown population means score.

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=480
Standard deviation( sd )=30
Sample Size(n)=25
Confidence Interval = [ 480 ± Z a/2 ( 30/ Sqrt ( 25) ) ]
= [ 480 - 1.96 * (6) , 480 + 1.96 * (6) ]
= [ 468.24,491.76 ]