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2. What percent of the area under the normal curve lies .. to the left of K + 20 ? b. to the right of m - 30 ? c. between M-T
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\\ X\sim N(\mu,\sigma^2) \\ P(\text{Area to the left of }\mu+2\sigma) \\ =P(X<\mu+2\sigma) \\=P(\frac{X-\mu}{\sigma}<2) \\=P(Z<2) \\=0.9772499

\\ P(\text{Area to the right of }\mu-3\sigma) \\ =P(X>\mu-3\sigma) \\=P(\frac{X-\mu}{\sigma}>-3) \\=P(Z>-3) \\= 1 - \Phi(-3) \\=0.9986501

\\ P(\text{Area between }\mu-\sigma \text{ and }\mu) \\ =P(\mu-\sigma<X<\mu) \\=P(-1<\frac{X-\mu}{\sigma}<0) \\=P(-1<Z<0) \\= \Phi(0) - \Phi(-1) \\=0.3413447

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