Answered: The size of fish is very important to…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm.

Round the probabilities to four decimal places.

It is possible with rounding for a probability to be 0.0000.

a) State the random variable.

  Select an answer rv X = the length of a randomly selected Atlantic cod rv X = the mean length of a sample of Atlantic cod rv X = the mean length of all Atlantic cod rv X = length is normally distributed rv X = a randomly selected Atlantic cod

b) Find the probability that a randomly selected Atlantic cod has a length of 47.08 cm or more.



c) Find the probability that a randomly selected Atlantic cod has a length of 50.48 cm or less.



d) Find the probability that a randomly selected Atlantic cod has a length between 47.08 and 50.48 cm.



e) Find the probability that randomly selected Atlantic cod has a length that is at least 62.99 cm.

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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