Probability Statistics (Question)

Question

The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal. Construct a 90% confidence interval for the population mean time to complete the forms. (Answer in 4 decimal places.) 

Answer: Blank 1 - Blank 2

Answer 1

n= 200

mean = 8.2

standard deviation= 2.2

90% confidence interval = 8.2 + and - 2.2z/sqr(n) where z is calculated from a z table or calculator z=about 1.6445 n=sample size

8.2 -2.2(1.6445/sqr200) to 8.2+2.2(1.6445)/sqr200

by the empirical rule z=about 2 for 95%

about 1 for 68%, so z is between 1 and 2 for 90%

by convention it's usually = 1.645 for 3 decimal places

8.2 -3.6179/sqr200 to 8.2+ 3.6179/sqr200

8.2-.2558 to 8.2 + .2558

the 90% confidence interval is about (7.9442, 8.4558 )