Introduction to Probability and Statistics

14th Edition

ISBN: 9781133103752

Author: Mendenhall, William

Publisher: Cengage Learning

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Textbook Question

Chapter 6.3, Problem 6.20E

Christmas Trees The diameters of Douglas firs grown at a Christmas tree farm are normally distributed with a mean of 4 inches and a standard deviation of 1.5 inches.

a. What proportion of the trees will have diameters between 3 and 5 inches?

b. What proportion of the trees will have diameters less than 3 inches?

c. Your Christmas tree stand will expand to a diameter of 6 inches. What proportion of the trees will not fit in your Christmas tree stand?

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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Chapter 6 Solutions

Introduction to Probability and Statistics

Ch. 6.3 - Consider a standard normal random variable with =0...Ch. 6.3 - Find these probabilities associated with the...Ch. 6.3 - Calculate the area under the standard normal curve...Ch. 6.3 - Calculate the area under the standard normal curve...Ch. 6.3 - Find the following probabilities for the standard...Ch. 6.3 - Find these probabilities for the standard normal...Ch. 6.3 - a. Find a z0 such that P(zz0)=.025 . b. Find a z0...Ch. 6.3 - Prob. 6.8E Ch. 6.3 - Prob. 6.9E Ch. 6.3 - a. Find a z0 such that P(z0zz0)=.90 . b. Find a z0...

Ch. 6.3 - Find the following percentiles for the standard...Ch. 6.3 - A normal random variable x has mean =10 and...Ch. 6.3 - Prob. 6.13E Ch. 6.3 - Prob. 6.14E Ch. 6.3 - A normal random variable x has mean 35 and...Ch. 6.3 - Prob. 6.16E Ch. 6.3 - A normal random variable x has an unknown mean and...Ch. 6.3 - Hamburger Meat The meat department at a local...Ch. 6.3 - Human Heights Human heights are one of many...Ch. 6.3 - Christmas Trees The diameters of Douglas firs...Ch. 6.3 - Cerebral Blood Flow Cerebral blood flow (CBF) in...Ch. 6.3 - Braking Distances For a car traveling 30 miles per...Ch. 6.3 - Elevator Capacities Suppose that you must...Ch. 6.3 - Sunflowers An experimenter publishing in the...Ch. 6.3 - Prob. 6.26E Ch. 6.3 - Prob. 6.27E Ch. 6.3 - Prob. 6.28E Ch. 6.3 - Prob. 6.30E Ch. 6.3 - How Many Words? A publisher has discovered that...Ch. 6.3 - Prob. 6.32E Ch. 6.4 - Consider a binomial random variable x with n=25...Ch. 6.4 - Prob. 6.36E Ch. 6.4 - Prob. 6.37E Ch. 6.4 - Let x be a binomial random variable with n=15 and...Ch. 6.4 - Let x be a binomial random variable with n=100 and...Ch. 6.4 - Prob. 6.40E Ch. 6.4 - Prob. 6.41E Ch. 6.4 - Prob. 6.42E Ch. 6.4 - Prob. 6.43E Ch. 6.4 - Prob. 6.44E Ch. 6.4 - Prob. 6.45E Ch. 6.4 - Prob. 6.46E Ch. 6.4 - No Shows Airlines and hotels often grant...Ch. 6.4 - Prob. 6.49E Ch. 6.4 - Pepsi’s Market Share Two of the biggest soft drink...Ch. 6.4 - Prob. 6.52E Ch. 6.4 - Prob. 6.53E Ch. 6 - Prob. 6.54SE Ch. 6 - Prob. 6.55SE Ch. 6 - Prob. 6.56SE Ch. 6 - Prob. 6.57SE Ch. 6 - a. Find a z0 such that P(z0zz0)=.95 . b. Find a z0...Ch. 6 - Prob. 6.59SE Ch. 6 - Let x be a binomial random variable with n=36 and...Ch. 6 - Prob. 6.61SE Ch. 6 - Prob. 6.62SE Ch. 6 - Prob. 6.63SE Ch. 6 - Prob. 6.64SE Ch. 6 - Prob. 6.65SE Ch. 6 - Prob. 6.66SE Ch. 6 - Prob. 6.67SE Ch. 6 - Prob. 6.68SE Ch. 6 - Prob. 6.69SE Ch. 6 - Used Cars A used-car dealership has found that the...Ch. 6 - Washers The life span of a type of automatic...Ch. 6 - Prob. 6.74SE Ch. 6 - Prob. 6.75SE Ch. 6 - Prob. 6.77SE Ch. 6 - Prob. 6.78SE Ch. 6 - Prob. 6.79SE Ch. 6 - Prob. 6.80SE Ch. 6 - No Shows An airline finds that 5% of the persons...Ch. 6 - Prob. 6.82SE Ch. 6 - Plant Genetics In Exercise 5.75, a cross between...Ch. 6 - Prob. 6.84SE Ch. 6 - Prob. 6.86SE Ch. 6 - Prob. 6.87SE Ch. 6 - Introvert or Extrovert? A psychological...Ch. 6 - Normal Distribution? The chest measurements for...Ch. 6 - Prob. 6.91SE Ch. 6 - Prob. 6.92SE Ch. 6 - Prob. 6.93SE Ch. 6 - Prob. 6.94SE Ch. 6 - Prob. 6.95SE Ch. 6 - Prob. 6.96SE Ch. 6 - Prob. 6.97SE

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Solution Summary: The author calculates the proportion of trees that have diameters between 3 and 5 inches. The proportion is 0.4972.

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Chapter 6 Solutions