Upper confidence limit value problem.

Assume a population is normally distributed. If the standard deviation of the population is 2.5, calculate the 95% confidence interval for mu when you take a sample of size 25 and get a sample mean of 5.24. Give the upper confidence limit value.

Is my answer correct? Please check it. Thank you.

My work:

Sample mean = 5.24

Standard deviation = 2.5

Standard error of mean = σ / √ n

Standard error of mean = 2.5 / √ 25

SE = 2.5/5

Standard error of mean 0.5

95 % Confidence interval:

5.24-(0.5)(1.96) and 5.24+(0.5)(1.96)

(4.26, 6.22)

**So, the upper confidence limit value is 6.22**