Specifications for a piece of material used in the manufacture of a bed mattress
ID: 360366 • Letter: S
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 51 and a standard deviation of 0.6 inches. The distribution of output is normal. Within what values will 84.34 percent of sample means fall, if samples of n = 14 are taken and the process is in control?
Question 5 options:
50.461 , 51.538
50.149 , 51.85
50.772 , 51.227
49.527 , 52.472
None of the Above
50.461 , 51.538
50.149 , 51.85
50.772 , 51.227
49.527 , 52.472
None of the Above
Explanation / Answer
Z value corresponding to 84.34% confidence level will be = 1.4166
Given are the following data :
Process Mean = m = 51
Standard deviation = Sd = 0.6
Sample size = n = 14
Thus control limits for 84.34% level of confidence are:
UCL ( Upper control limit) = M + Z x Sd /Square root ( n)
= 51 + 1.4166 x 0.6 / Square root ( 14 )
= 51 + 1.4166 x 0.6 /3.741
= 51 + 0.2272
= 51 .2272
LCL ( Lower control limit) = M - Z x Sd /Square root ( n)
= 51 - 1.4166 x 0.6 / Square root ( 14 )
= 51 - 1.4166 x 0.6 /3.741
= 51 - 0.2272
= 51 - 0.2272
= 50.7728
ANSWER : 50.772 , 51.227
ANSWER : 50.772 , 51.227
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