You are participating in a fishing competition in a lake in Michigan. The organizer announces that competitors must catch a fish that is heavier than 95% of the other competitors' submissions to win a prize. The population mean weight of the fish in the lake is 8 kg, and the population variance is 4 kg². Each competitor is allowed to submit only one fish to preserve the environment, and they can only submit once. Three competitors—Alan, Mary, and Jane—each make different assumptions about the distribution of fish weights in the lake. They catch fish until getting one that is heavier than the 95th percentile under their model. (a) (8pts) Alan assumes the fish weights follow a uniform distribution. Find the 95th percentile of the fish weights. Assume the weights are uniformly distributed between a and b, with the same mean, 8 kg, and variance, 4 kg², as given. (Hints: You need to find a and b.) (b) (4 pts) Mary assumes the fish weights follow a normal distribution. Find the 95th percentile of the fish weights. Use the population mean, 8 kg, and variance, 4 kg², provided. (Hints: You need to do un-standardization.) (c) (6 pts) Jane assumes the fish weights follow an exponential distribution. Find the 95th percentile of the fish weights. As exponential distribution has one parameter, use the exponential distribution with the same mean of 8 kg, as given. (Hints: You need to find λ) (d) (2 pts) Based on the results from parts a), b), and c), whose assumption (Alan's, Mary's, or Jane's) makes the most sense? Justify your answer considering the characteristics of the distributions.
You are participating in a fishing competition in a lake in Michigan. The organizer announces that competitors must catch a fish that is heavier than 95% of the other competitors' submissions to win a prize. The population mean weight of the fish in the lake is 8 kg, and the population variance is 4 kg². Each competitor is allowed to submit only one fish to preserve the environment, and they can only submit once. Three competitors—Alan, Mary, and Jane—each make different assumptions about the distribution of fish weights in the lake. They catch fish until getting one that is heavier than the 95th percentile under their model. (a) (8pts) Alan assumes the fish weights follow a uniform distribution. Find the 95th percentile of the fish weights. Assume the weights are uniformly distributed between a and b, with the same mean, 8 kg, and variance, 4 kg², as given. (Hints: You need to find a and b.) (b) (4 pts) Mary assumes the fish weights follow a normal distribution. Find the 95th percentile of the fish weights. Use the population mean, 8 kg, and variance, 4 kg², provided. (Hints: You need to do un-standardization.) (c) (6 pts) Jane assumes the fish weights follow an exponential distribution. Find the 95th percentile of the fish weights. As exponential distribution has one parameter, use the exponential distribution with the same mean of 8 kg, as given. (Hints: You need to find λ) (d) (2 pts) Based on the results from parts a), b), and c), whose assumption (Alan's, Mary's, or Jane's) makes the most sense? Justify your answer considering the characteristics of the distributions.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.5: Interpreting Data
Problem 3E
Related questions
Question
Statistics and
Transcribed Image Text:You are participating in a fishing competition in a lake in Michigan. The organizer
announces that competitors must catch a fish that is heavier than 95% of the other
competitors' submissions to win a prize. The population mean weight of the fish in the lake
is 8 kg, and the population variance is 4 kg². Each competitor is allowed to submit only one
fish to preserve the environment, and they can only submit once.
Three competitors—Alan, Mary, and Jane—each make different assumptions about the
distribution of fish weights in the lake. They catch fish until getting one that is heavier than
the 95th percentile under their model.
(a) (8pts) Alan assumes the fish weights follow a uniform distribution. Find the 95th
percentile of the fish weights. Assume the weights are uniformly distributed
between a and b, with the same mean, 8 kg, and variance, 4 kg², as given. (Hints: You
need to find a and b.)
(b) (4 pts) Mary assumes the fish weights follow a normal distribution. Find the 95th
percentile of the fish weights. Use the population mean, 8 kg, and variance, 4 kg²,
provided. (Hints: You need to do un-standardization.)
(c) (6 pts) Jane assumes the fish weights follow an exponential distribution. Find the
95th percentile of the fish weights. As exponential distribution has one parameter,
use the exponential distribution with the same mean of 8 kg, as given. (Hints: You
need to find λ)
(d) (2 pts) Based on the results from parts a), b), and c), whose assumption (Alan's,
Mary's, or Jane's) makes the most sense? Justify your answer considering the
characteristics of the distributions.
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 2 steps
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
