Amanufacturing process is designed to produce bolts with a 0.5-inch diameter. once each day, a random sample of 36 bolts is selected and the bolt diameters recorded. if the resulting sample mean is less than 0.490 inches or greater than 0.510 inches, the process is shut down for adjustment. the standard deviation for diameter is 0.02 inches 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 0.5 inches. round your answer to four decimal places.)

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)

step-by-step explanation:

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.