(1 point) The heights of all men in a large population follow a Normal distribut

Question

(1 point) The heights of all men in a large population follow a Normal distribution with unknown mean ? and standard deviation ?-2.23 inches. A simple random sample of 130 men produced a mean height of x 66.1 inches. In each question below, give answers to at least three decimal places. a. Find a 90% confidence interval for ti, using the above sample data: b. Find a 95% confidence interval for A1, using the above sample data: c. Find a 99% confidence interval for,1, using the above sample data: Note: You can earn nartial credit on this oroblem

Explanation / Answer

Solution:- Given that ? = 2.23 , n = 130 , x - bar = 66.1

Z Score => 90% 95% 99% ---> 1.645 1.96 2.576

a) 90% confidence interval for the ? = X +/- z*? /sqrt(n)
= 66.1 +/-1.645*2.23/sqrt(130)
= 65.778 , 66.422

b) 95% confidence interval for the ? = 66.1 +/-1.96*2.23/sqrt(130)
= 65.717 , 66.483

c) 99% confidence interval for the ? = 66.1 +/-2.576*2.23/sqrt(130)
= 65.596 , 66.604

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