Question

2. A random variable is normally distributed s normally distributed with a mean of u = 50 and a standard deviation of o = 5. a. Sketch a normal curve for the probability density 50, 55, 60, and 65. of the probability density function. Label the horizontal axis with values of 35, 40, 45, b. What is the probability that the rando Tobability that the random variable will assume a value between 45 and 55? Empirical Rule. c. What is the probability that the random Is the probability that the random variable will assume a value between 40 and 60? Empirical Rule. is the probability that the random variable will assume a value between 35 and 657 Empirical Rule. e. What is the probability that the random variable will assume a value 60 or more? naf is the probability that the random variable will assume a value between 40 and 55? 2. What is the probability that the random variable will assume a value between 35 and 40?

Answer 1

4 = SO , = S 14.12: 35 40 4-30 4-2- 45 u-r 4:50 u 55 60 65 uto utas u+30 68.27.1 95.45%. (b) P (Between 45 and 55) It is one within one standard deviation . use empirical rule P = 0.6827 (C) PC Between 40 and 60) 1. It is within a standard deviation, we empirical lule P = 0.9545 (d) PC Between 35 and 65 ) It is within 3 standard deviation, we empirical sule - f = 0.9972 ce) P (60 or more) P(x260) = 1 - P(x<60) = 1-(2< x-u) I-Plz < 60-90 Ics Scanned with CamScanner 5

= 1 - Plzco) = O - 0.9772 = 0.0228 As C®) P(Between 40 and 55) P(40<x<55) = P( Mode < za kate) = P(40.90 < z< $5=50) =plq<2<1) = P(Z<1) - P(Z2-2) = 0.0413 - 0.0220 - 0.8186. Ang (9) P (Between 35 and 40) P(35 < x <40) = P(x-" <za tl) = P( 35370 < 2 < 4025 = P(-3(-3) - P(26-2) = 0.0214 Ang A Scanned with CamScanner