Question

Specifications for a piece of material used in the manufacture of a bed mattress require that the piece be between a Lower and Upper value (in inches) centered around the process mean. The process that produces the piece yields a mean of 49 and a standard deviation of 1 inches. The distribution of output is normal. Within what values will 91.83 percent of sample means fall, if samples of n = 8 are taken and the process is in control?

Question 2 options:

	47.821 , 50.178
	48.384 , 49.615
	46.133 , 51.866
	47.258 , 50.741
	None of the Above

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 49

Population standard deviation =    = 1

Sample size = n = 8

At 91.83% confidence level

= 1 - 91.83%  

= 1 - 0.9183 = 0.0817

/2 = 0.04085

Z/2 = Z0.04085  = 1.741

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

= 1.741 * ( 1 /  8 )

= 0.6155

At 91.83% confidence interval estimate of the population mean is,

  ± E

49 ± 0.6155   

( 48.384, 49.615 )