A manufacturing process is designed to produce bolts with a 0.5-in. diameter. On
ID: 3160567 • Letter: A
Question
A manufacturing process is designed to produce bolts with a 0.5-in. diameter. Once each day, a random sample of 36 bolts is selected and the diameters recorded. If the resulting sample mean is less than 0.480 in. or greater than 0.520 in., the process is shut down for adjustment. The standard deviation for diameter is 0.04 in. A) describe the sampling mean, variance, standard deviation, and shape. B) What is the probability that the manufacturing line will be shut down unnecessarily? A manufacturing process is designed to produce bolts with a 0.5-in. diameter. Once each day, a random sample of 36 bolts is selected and the diameters recorded. If the resulting sample mean is less than 0.480 in. or greater than 0.520 in., the process is shut down for adjustment. The standard deviation for diameter is 0.04 in. A) describe the sampling mean, variance, standard deviation, and shape. B) What is the probability that the manufacturing line will be shut down unnecessarily?Explanation / Answer
A manufacturing process is designed to produce bolts with a 0.5-in. diameter. Once each day, a random sample of 36 bolts is selected and the diameters recorded. If the resulting sample mean is less than 0.480 in. or greater than 0.520 in., the process is shut down for adjustment. The standard deviation for diameter is 0.04 in.
A) describe the sampling mean, variance, standard deviation, and shape.
Mean =0.5
Variance = 0.00004444
Standard deviation =0.0067
The is approximately normal because sample size > 30.
B) What is the probability that the manufacturing line will be shut down unnecessarily?
Z value for 0.48, z =(0.48-0.5)/0.0067 = -2.99
Z value for 0.52, z=(0.52-0.5)/0.0067 = 2.99
P( x <0.480 or x >0.520)
=( z < -2.99) +P( z >2.99)
=0.0014 +0.0014
=0.0028
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