Question

5. A machine is producing metal cans that are cylindrical in shape. A sample of 12 cans are taken and the average diameter was found to be 10 mm. Find a 95 percent confidence interval for the mean diameter of pieces for this machine. Assume a normal distribution. standard Deviation was 0.282.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 10

Population standard deviation =    = 0.282

Sample size = n = 12

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

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

= 1.96 * ( 0.282 /   12)

= 0.16

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

  ± E

10 ± 0.16

( 9.84 , 10.16)