Recall that the 100pth percentile of a continuous random var

Recall that the (100p)^th percentile of a (continuous) random variable with cdf F is the real number x_p such that F(x_p) = p. Show that (100p)^th percentile of N (mu, sigma^2) = mu + sigma (100p)^th percentile of N(0, 1). Let Z ~ N(0, 1) and alpha (0, 1). We denote by z_alpha (100(1 - alha)^th percentile of Z: that is the real number that satisfies P(Z > z_alpha) = alpha. This notation will be extensively used in Statistics. See pg. 109. Show that -Z_alpha is the (100 alpha)^th percentile of N(0, 1) and find z_alpha for alpha = 10%, 5%, 1%. Suppose that the LSAT score of a randomly chosen entering student in a law school class is normally distributed with mean 160 and standard deviation 10. What is the LSAT score that a randomly chosen student should have in order to be in the top 10%?

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