University:
University of Houston
Course:
MATH 1313 | Linear Algebra
Academic year:

2022
Views:

271

Pages:

8
Author:

Bohrrechtx9nb

Page 1: Using Table A Heading: Example: Using Table A, find the following probabilities: A. P(Z < -1.34) = 0.0901 B. P(Z < 2.02) = 0.9783 C. P(Z > 1.35) = 1 - P(Z < 1.35) = 1 - 0.9115 = 0.0885 D. P(-1.34 < Z < 2.02) = P(Z < 2.02) - P(Z < -1.34) = 0.9783 - 0.0901 = 0.8882 Now let's repeat with calculator and R-Studio. μ = 0, σ = 1 Page 2: Standardizing X Heading: If we want to use the table for probabilities and are not given z, we must compute the z-score using the formula above. Example: If X has distribution N(90,12), standardize X and use Table A to find the following probabilities. A. P(X < 80) = P(Z < (80-90)/12) = P(Z < -0.83) = 0.203 B. P(X > 95) normcdf (95,100000, 90, 12) = 0.338 pnorm(.83) = 0.2032894 pnorm(90,12) = 0.338 C. P(80 < X < 95) = .459 P(X < 95) - P(X < 80) normcdf (-10000, 95, 90, 12) = 0.545973 normcdf (-10000, 80, 90, 12) Using the calculator and R, it's a bit easier Use code with caution. R-Studio: P(X < x) = pnorm (x, mean, sd) Ti-83/84: normalcdf(low, high, mean, sd) P(X > #) = 1 - pnorm(#, mean, sd) diagram included comparing normalcdf to R. Use code with caution. Page 3: More Examples More Examples: "The length of time needed to complete a certain test is normally distributed with mean 24 minutes and standard deviation 11 minutes. Find the probability that it will take less than 40 minutes to complete the test." μ = 24 , σ = 11 P(X < 40) normalcdf (-10000, 40, 24, 11) pnorm (40, 24, 11) = 0.927 "If X is normally distributed with a mean of 30 and a standard deviation of 2, find P(30 < X < 33.4)." diagram showing the area under the curve for x 30 to x = 33.4 normalcdf (30, 33.4, 30, 2) - pnorm (30, 30, 2) pnorm (33.4, 30, 2) - pnorm(30, 30, 2) = 0.455 "Suppose that X is normally distributed with a mean of 60 and a standard deviation of 9. What is P(X ≥ 68.73)?" * normalcdf(68.73, 100000, 60, 9) = 1 - pnorm(68.73, 60, 9) * >1 - pnorm (68.73,60,9) = 0.1735 Page 4: Inverse and Popper "Find a value of c so that P(Z ≤ c) = 0.47." invNorm (.47, 0, 1) diagram showing the syntax. * = -0.07526 >qnorm(.47) = -0.0752698 Popper 07 4. "A normal density curve has which of the following properties?" * d. All of the properties above are correct. 5. "The area under the standard normal curve corresponding to -0.3 < Z < 1.6 is" * a. 0.3273 * same as asking P(-.3 < Z < 1.6)