A machine producer that are cylindrical in shape A sample of

A machine producer that are cylindrical in shape. A sample of these paces is taken, and diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 1.01, and 1.03 assume the population is normally distributed. Find a 99% confidence interval for the mean diameter what is ? what is s ? is a random variable of the amount of time a car opens at a drive thru banks teller is normally distributed with a mean of 3.2 minutes and standard deviation of 1.6 minutes.

Solution

A) X-BAR = 1.0075......S= s.d / sqrt(8) = 0.009014.........z-score for 99% confience interval= 2.575829......

1)99% confidence interval = [ 1.0075 - ( 2.575829 * 0.009014) , 1.0075 + (  2.575829 * 0.009014 ) ]........
= [ 0.9842815 , 1.030719 ]............

2) X-bar~N(3.2, 1.6).....N = 64...Standard error = 1.6 / sqrt(64) = 0.2......
a) p ( x-bar < 2.7 ) = p ( z < (2.7 - 3.2) / 0.2 )= p ( z < -2.5) = 0.006209665

b) p( x-bar > 3.5) = p ( z > (3.5 - 3.2) / 0.2 ) = 1 - p( z < 1.5 ) = 0.0668072.....

c) p ( 3.2 < x-bar < 3.4 ) = p( 0 < z < (3.4-3.2)/ 0.2 ) = p ( z < 1) - p (z < 0) =  0.8413447 - 0.5 = 0.3413447......

3) population variance = 8...and n=20.......and chi-sq value for s^2>20 with 19 d.f = 0.6054218
p( s^2 >20) = 1 - p [ s^2 <20 ] = 1 - [ 8* 0.6054218 / 19 ] = 0.7450856....

4) proportion = 532 / 1100 = 0.4836364.....
sample sd = sqrt [ 0.4836364*(1 - 0.4836364) / 1100 ] =  0.01506749.........

z-score for 95% confidence interval = 1.96...
confidence interval = [ 0.4836364 - ( 1.96 * 0.01506749) ,  0.4836364 + ( 1.96 * 0.01506749) ]........
= [ 0.4541041 , 0.5131687 ]........

Between 0.45 and 0.51 is the proportion of people answer that they favor a flat income tax....