The random variable M M\,M represents the mass, in grams, of a synthetic gemstone produced in a laboratory. It is known that M M\,M follows a normal distribution with mean 60 and standard deviation 15.
Determine the probability that a randomly selected gemstone has a mass greater than 84 g.
Find the value of k k\,k such that
P(60−k<M<60+k)=0.90 P(60 - k < M < 60 + k) = 0.90 P(60−k<M<60+k)=0.90A single observation mmm, of MMM, is taken. A rectangular label for the gemstone's display case is designed on a coordinate grid with vertices at (0,0)(0, 0)(0,0), (m,0)(m, 0)(m,0), (m,m−20)(m, m - 20)(m,m−20) and (0,m−20)(0, m - 20)(0,m−20), where the units are centimetres.
Find the probability that the area of this label is more than 1500 cm2.