Question

A manufacturing process is designed to produce bolts with a 0.25-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 0.230 in. or greater than 0.270 in., the process is shut down for adjustment. The standard deviation for diameter is 0.04 in. What is the probability that the manufacturing line will be shut down unnecessarily? (Hint: Find the probability of observing an x in the shutdown range when the true process mean really is 0.25 in. Round your answer to four decimal places.)

Answer 1

Answer:

0.6170

Step-by-step explanation:

Given that a manufacturing process is designed to produce bolts with a 0.25-in. diameter.

i.e. no of bolts which are produced as per standard is X means then

X is normal with mean = 0.250 and std dev = 0.04

No of bolts tested = 36

If this mean falls outside the interval (0.230,0.270) the production would be shut down.

i.e. P(|x-25|>0.20) =production shut down probability

$P(|x-25|>0.20)\\=P(|Z|>0.5)\\=2(0.5-0.1915)\\= 0.6170$