The lifetime of a lightbulb in a certain application is normally distributed with mean μ = 1400 hours and standard deviation σ = 200 hours. 
   a.What is the probability that a lightbulb will last more than 1800 hours? 
 b.Find the 10th percentile of the lifetimes.
 c.A particular lightbulb lasts 1645 hours. What percentile is its lifetime on?
 d.What is the probability that the lifetime of a lightbulb is between 1350 and 1550 hours?

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Temperature effects on atom arrangements

Atoms are the smallest units of matter. Atoms can be subdivided into electrons, protons, and several other subatomic particles. Groups or combinations of atoms form molecules that primarily decide the property and behavior of materials. These molecules have the property to attract other molecules based on the valence electrons in the atoms' outermost orbit. An orderly arrangement of molecules is known as crystal structure, which forms the fundamental topic of concern in materials science and engineering. The arrangement of molecules is different for different materials and hence, each material exhibits different lattice arrangements. The lattice arrangements are functions of external loads, deformations, and temperature. On experiencing high temperatures or low temperatures, the behavior of the lattice arrangement of a material change.