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1. If X ~ N(200,2²), find а) Р(X < 197) b) Р(Х < 200 .5)

1. If X ~ N(200,2²), find а) Р(X < 197) b) Р(Х < 200 .5)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. If X - N(200,2²), find а) Р(X < 197) b) Р(X < 200.5) 2. Let x be a continuous random variable that is normally distributed with a mean of 80 and a standard deviation of 12. Find the probability that x assumes a value a. greater than 69 c. greater than 101 b. less than 73 d. less than 87 3. Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 29 and 36 b. between 22 and 35 4. Let X denote the time taken to run a road race. X is normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a. in less than 160 minutes? b. in 215 to 245 minutes?
Transcribed Image Text:1. If X - N(200,2²), find а) Р(X < 197) b) Р(X < 200.5) 2. Let x be a continuous random variable that is normally distributed with a mean of 80 and a standard deviation of 12. Find the probability that x assumes a value a. greater than 69 c. greater than 101 b. less than 73 d. less than 87 3. Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 29 and 36 b. between 22 and 35 4. Let X denote the time taken to run a road race. X is normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a. in less than 160 minutes? b. in 215 to 245 minutes?
5. A construction zone on a highway has a posted speed limit of 40 miles per hour. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 46 miles per hour and a variance of 16 miles per hour. Find the percentage of vehicles passing through this construction zone that are a. exceeding the posted speed limit b. traveling at speeds between 50 and 57 miles per hour.
Transcribed Image Text:5. A construction zone on a highway has a posted speed limit of 40 miles per hour. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 46 miles per hour and a variance of 16 miles per hour. Find the percentage of vehicles passing through this construction zone that are a. exceeding the posted speed limit b. traveling at speeds between 50 and 57 miles per hour.
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