Question #1 Lab 11Instructions: For this lab, your solutions should be written or typed up neatly and uploaded toCanvas as PDF, document, or image scan.In probability theory, the normal distribution (also known as a Gaussian distribution or bellcurve) is a commonly used probability distribution. Normal distributions are important instatistics and are often used in the natural and social sciences to represent real-valued randomvariables whose distributions are not known specifically. Describing the normal distributionusing a mathematical function (called a probability distribution function) is given:f(x)1O√2π-(x-μ)²e 20²P(a ≤ x ≤ b) =The area underneath a probability density function corresponds with the probability of the event occurring:=f²fcf(x) dxThe main mathematical issue with the normal distribution is that the function fe-x² dx has no elementarysolution. So, how can we solve the area under the curve if we can't solve the integral? We must take anotherapproach. In many cases where f has no elementary antiderivative, we are able to take f and convert it intoan infinite power series. This is the fundamental idea behind Taylor and Maclaurin series. We will bediscussing this approach in lab and class this week. Here is the problem that you will be solving:The lengths of a certain population of Atlantic croaker fish are normally distributed with an average lengthof μ = 10 inches and a standard deviation of a = 2 inches. In each part, your goal is to determine howmany terms are needed to insure a result accurate to at least 0.1%.1. Find the probability that a randomly selectedcroaker fish from this population will be betweena = 11 inches and ß = 13 inches long.2. Find the probability that a randomly selectedcroaker fish from this population will be less thanB = 8 inches long (use a = 0).3. In a statistics course, this type of question can besolved by using a "Z-score" and "Z-table" or byusing a "Probability Calculator." Use a probabilitycalculator to check your solutions.(Here is one: https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php)25.2015+.10Normal Distribution FunctionThe mean of the distributionThe standard deviation+.05+-.05-.10910111213✓ You are encouraged to use wxMaxima to integrate f's Maclaurin series and calculate theprobabilities to the desired level of accuracy!

Mean μ=10 Standard deviation σ=2

1. Find the probability that a randomly selected croaker fish from this population will be between a = 11 inches and ß = 13 inches long. 2. Find the probability that a randomly selected croaker fish from this population will be less than B = 8 inches long (use a = 0). 3. In a statistics course, this type of question can be solved by using a "Z-score" and "Z-table" or by using a "Probability Calculator." Use a probability calculator to check your solutions. (Here is one: https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php) 25 .20 -.15 +.10 .05 .05 -.10 10 11 12 13

1. Find the probability that a randomly selected croaker fish from this population will be between a = 11 inches and ß = 13 inches long. 2. Find the probability that a randomly selected croaker fish from this population will be less than B = 8 inches long (use a = 0). 3. In a statistics course, this type of question can be solved by using a "Z-score" and "Z-table" or by using a "Probability Calculator." Use a probability calculator to check your solutions. (Here is one: https://www.mathportal.org/calculators/statistics-calculator/normal-distribution-calculator.php) 25 .20 -.15 +.10 .05 .05 -.10 10 11 12 13

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...

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