Suppose taxi time, a, at airport A is normally distributed with mean of 27 minutes and standard deviation 8 minutes; taxi time, b, at airport B is normally distributed with mean of 39 minutes and standard deviation 12 minutes; taxi time, c, at airport C is normally distributed with mean of 41 minutes and standard deviation 10 minutes. JJ Airlines has a plane flying to airport A, airport B, and airport C on Sunday. Airport A charges $131 per minute of taxi time; airport B charges $150 per minute of taxi time; airport c charges $200 per minute of taxi time. Let X = total amount of taxi time in minutes for the JJ plane. Let W = total taxi charges for the JJ plane. X is defined as X = a + b + c. W = 131a + 150b + 200c. Note that a, b, and c are independent of one another. d) Calculate the standard deviation of W. e) If we pick a value k such that the probability that X > k equals .25 then calculate k. f) JJ Airlines has $20,000 available to pay for taxi time? What is the probability that JJ has enough to pay the total taxi time bill on Sunday?

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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An airline is charged by an airport based upon the total taxi-time that an airplane spends to take off and land. Suppose taxi time, a, at airport A is normally distributed with mean of 27 minutes and standard deviation 8 minutes; taxi time, b, at airport B is normally distributed with mean of 39 minutes and standard deviation 12 minutes; taxi time, c, at airport C is normally distributed with mean of 41 minutes and standard deviation 10 minutes. JJ Airlines has a plane flying to airport A, airport B, and airport C on Sunday. Airport A charges $131 per minute of taxi time; airport B charges $150 per minute of taxi time; airport c charges $200 per minute of taxi time. Let X = total amount of taxi time in minutes for the JJ plane. Let W = total taxi charges for the JJ plane. X is defined as X = a + b + c. W = 131a + 150b + 200c. Note that a, b, and c are independent of one another.

d) Calculate the standard deviation of W.

e) If we pick a value k such that the probability that X > k equals .25 then calculate k.

f) JJ Airlines has $20,000 available to pay for taxi time? What is the probability that JJ has enough to pay the total taxi time bill on Sunday?

g) What is the probability that X is within two standard deviations of its expected value?

h) What is the probability that a is greater than b?

i) What is the probability that a, b, and c are all less than their 50th percentiles?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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