Question

Determine the 95​% confidence interval estimate for the population mean of a normal distribution given n=144​, sigma=105​, and x overbar=1,200. The 95​% confidence interval for the population mean is from to . ​(Round to two decimal places as needed. Use ascending​ order.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 1200

Population standard deviation = = 105

Sample size = n = 144

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96 * (105 / 144 )

= 17.15

At 95% confidence interval estimate of the population mean is,

- E < < + E

1200 - 17.15 < < 1200 + 17.15

1182.85 < < 1217.15

( 1182.85 , 1217.15 )