A machine fills coke into bottles automatically. Actual volumes are normally distributed with µ = 500 ml and o 10 ml. (i) Determine the probability that the bottles are filled within the tolerance limit of 485 ml to 515 ml. (ii) Suppose the mean remains the same. Determine the change needed in the standard deviation if 95% of the bottles must be within the tolerance limit of 485 ml to 515 ml.
A machine fills coke into bottles automatically. Actual volumes are normally distributed with µ = 500 ml and o 10 ml. (i) Determine the probability that the bottles are filled within the tolerance limit of 485 ml to 515 ml. (ii) Suppose the mean remains the same. Determine the change needed in the standard deviation if 95% of the bottles must be within the tolerance limit of 485 ml to 515 ml.
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
![(a) A machine fills coke into bottles automatically. Actual volumes are normally distributed
with u = 500 ml and o = 10 ml.
(i) Determine the probability that the bottles are filled within the tolerance limit of 485
ml to 515 ml.
(ii) Suppose the mean remains the same. Determine the change needed in the standard
deviation if 95% of the bottles must be within the tolerance limit of 485 ml to 515 ml.
(b) It was found that an exponential distribution with a mean of 5 minutes was suitable to
model the duration of a visitor at a website.
(i) Find the probability that the website is viewed for at least 3 minutes.
(ii) If the website has already been viewed for 1.5 minutes, find the probability that the
home page is viewed for an additional 0.5 minutes.
(c) Jones figures that the total number of thousands of miles that an auto can be driven before
it would need to be junked is uniformly distributed over [0, 40]. Smith has a used car that
he claims has been driven only 10,000 miles. If Jones purchases the car, determine the
probability that she would get at least 20,000 additional miles out of it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06ea494c-30b2-4250-baa3-10a4f8ba75e8%2Ff041eb20-19b6-40e0-a8ac-9008ac5a76a4%2Fej18bzg_processed.png&w=3840&q=75)
Transcribed Image Text:(a) A machine fills coke into bottles automatically. Actual volumes are normally distributed
with u = 500 ml and o = 10 ml.
(i) Determine the probability that the bottles are filled within the tolerance limit of 485
ml to 515 ml.
(ii) Suppose the mean remains the same. Determine the change needed in the standard
deviation if 95% of the bottles must be within the tolerance limit of 485 ml to 515 ml.
(b) It was found that an exponential distribution with a mean of 5 minutes was suitable to
model the duration of a visitor at a website.
(i) Find the probability that the website is viewed for at least 3 minutes.
(ii) If the website has already been viewed for 1.5 minutes, find the probability that the
home page is viewed for an additional 0.5 minutes.
(c) Jones figures that the total number of thousands of miles that an auto can be driven before
it would need to be junked is uniformly distributed over [0, 40]. Smith has a used car that
he claims has been driven only 10,000 miles. If Jones purchases the car, determine the
probability that she would get at least 20,000 additional miles out of it.
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 3 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.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