1. The outer diameter of an arrowis nominally 20 cm. The diameter is normally distributed with mean 20cm and standard deviation 1.25 cm. If the actual diameter deviates from the nominal by more than 2 cm and by less than 4 cm, the manufacturer loses 150 pesos. If the difference is more than 5cm, the manufacturer loses 350 pesos. A) Find the maximumdiameter of 95% of the arrows B) Find the minimum diameter of 8% of the arrows C) Find the probability distribution function of the random variable "manufacturer's loss" D) Find the mean and standard deviation of the manufacturer's loss E) How should the standard deviation be adjusted so that there is only loss in 1% of the arrows? 2- The time in seconds it takes to connecta server on a weekdayfollows a Weibull distribution with a = 0.6"and" B = 0.25. At the weekend it has the same distribution with parameters a = 0.24 "and" B = 1. A) Calculate the difference between the mean response time between the week and the weekend. B) Calculate the probability that during the week, the connection takes more than 10 seconds. C) Calculate the probability that on the weekend, the connection takes more than 10 seconds. D) If we have been waiting more than 3 minutes forthe connection, ittakes more than 10 seconds to make a connection. E) What is the maximum time of 90% of the connections?
1. The outer diameter of an arrowis nominally 20 cm. The diameter is normally distributed with mean 20cm and standard deviation 1.25 cm. If the actual diameter deviates from the nominal by more than 2 cm and by less than 4 cm, the manufacturer loses 150 pesos. If the difference is more than 5cm, the manufacturer loses 350 pesos. A) Find the maximumdiameter of 95% of the arrows B) Find the minimum diameter of 8% of the arrows C) Find the probability distribution function of the random variable "manufacturer's loss" D) Find the mean and standard deviation of the manufacturer's loss E) How should the standard deviation be adjusted so that there is only loss in 1% of the arrows? 2- The time in seconds it takes to connecta server on a weekdayfollows a Weibull distribution with a = 0.6"and" B = 0.25. At the weekend it has the same distribution with parameters a = 0.24 "and" B = 1. A) Calculate the difference between the mean response time between the week and the weekend. B) Calculate the probability that during the week, the connection takes more than 10 seconds. C) Calculate the probability that on the weekend, the connection takes more than 10 seconds. D) If we have been waiting more than 3 minutes forthe connection, ittakes more than 10 seconds to make a connection. E) What is the maximum time of 90% of the connections?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Ñ2
Transcribed Image Text:1. The outer diameter of an arrow is nominally 20 cm. The diameter is normally distributed with
mean 20cm and standard deviation 1.25 cm. If the actual diameter deviates from the nominal by
more than 2 cm and by less than 4 cm, the manufacturer loses 150 pesos. If the difference is more
than 5cm, the manufacturer loses 350 pesos.
A) Find the maximumdiameter of 95% of the arrows
B) Find the minimum diameter of 8% of the arrows
C) Find the probability distribution function of the random variable "manufacturer's loss"
D) Find the mean and standard deviation of the manufacturer's loss
E) How should the standard deviation be adjusted so that there is only loss in 1% of the arrows?
2. The time in seconds it takes to connecta server on a weekdayfollows a Weibull distribution with
a = 0.6 "and" B = 0.25. At the weekend it has the same distribution with parameters a= 0.24 "and" B
= 1.
A) Calculate the difference between the mean response time between the week and the weekend.
B) Calculate the probability that during the week, the connection takes more than 10 seconds.
C) Calculate the probability that on the weekend, the connection takes more than 10 seconds.
D) If we have been waiting more than 3 minutes for the connection, ittakes more than 10 seconds
to make a connection.
E) What is the maximum time of 90% of the connections?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON