Explanation Given Information: In a political poll, where the probability that each person will tell his or her preference is 90 % . Total number of persons polled are 1000 out of which 51 % prefer candidate Goode and 49 % prefer Slick. Formula Used: If there are n independent trails associated with the binomial variable X, and probability of success is p, then the expected value of X is given by, E ( X ) = n p If there are n independent trails associated with the binomial variable X, and probability of success is p, and probability of failure is q then the variance and standard deviation of X is given by, σ 2 = n p q and σ = n p q If there are n independent trails associated with the binomial variable X, and probability of success is p, and probability of failure is q and the interval in which the values of X will fall is within three standard deviations of the mean in the range of 0 to n, then P ( a ≤ X ≤ b ) ≈ P ( a − 0.5 ≤ Y ≤ b + 0.5 ) If the mean and standard deviation of X with normal distribution are μ and σ , and Z is the standard normal variable, then the rule for probability is given by, P ( X ≥ a ) = P ( Z ≥ a − μ σ ) Calculation: Consider the probability of success that a person prefers Goode. Total number of persons polled are, n = 1000 Total number of people tell their preference, .9 out of which 49 % prefer Goode. Remaining number of people who did not tell their preference is .1 out of which 51 % prefer Goode. Evaluate the probability of success, p p = .9 × .49 + .1 × .51 = .441 + .051 = .492 Evaluate the probability of failure, q q = 1 − .492 = .508 Evaluate the expected value of X using the formula E ( X ) = n p E ( X ) = 1000 × 0.492 E ( X ) = 492 Evaluate the variance of the random variable, using the formula σ 2 = n p q σ 2 = 1000 × 0.492 × 0.508 σ 2 = 249.936 Evaluate the square root of the variance to determine the standard deviation. σ 2 = 249.936 σ = 249.936 σ ≈ 15.809 Goode will do at least well, if Goode will poll at least 51 % out of 1000 persons

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Chapter 8.5, Problem 64E

To determine

To calculate: The approximate probability such that Goode will do at least well where 49% prefer Goode in a political poll, where the probability that each person will tell his or her preference is 90%. Total number of persons polled are 1000 out of which 51% prefer candidate Goode and 49% prefer Slick.

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Prob. 11E Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Prob. 13E Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Find the probability that a normal variable takes...Ch. 8.5 - Find the probability that a normal variable takes...Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Suppose X is a normal random variable with mean...Ch. 8.5 - Suppose X is a normal random variable with mean...Ch. 8.5 - Prob. 22E Ch. 8.5 - If you roll a die 100 times, what is the...Ch. 8.5 - If you roll a die 100 times, what is the...Ch. 8.5 - If you roll a die 200 times, what is the...Ch. 8.5 - Prob. 26E Ch. 8.5 - SAT Scores SAT test scores are normally...Ch. 8.5 - Prob. 28E Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - SAT Scores SAT test scores are normally...Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - Baseball The mean batting average in major league...Ch. 8.5 - Baseball The mean batting average in major league...Ch. 8.5 - Prob. 39E Ch. 8.5 - Marketing Your hot sauce company rates its sauce...Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Distribution of Income If we model after-tax...Ch. 8.5 - Prob. 46E Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Prob. 51E Ch. 8.5 - Prob. 52E Ch. 8.5 - Prob. 53E Ch. 8.5 - Prob. 54E Ch. 8.5 - Prob. 55E Ch. 8.5 - Prob. 56E Ch. 8.5 - Prob. 57E Ch. 8.5 - Prob. 58E Ch. 8.5 - Aviation The probability of a plane crashing on a...Ch. 8.5 - Prob. 60E Ch. 8.5 - Prob. 61E Ch. 8.5 - Prob. 62E Ch. 8.5 - Prob. 63E Ch. 8.5 - Prob. 64E Ch. 8.5 - Prob. 65E Ch. 8.5 - Prob. 66E Ch. 8.5 - Prob. 67E Ch. 8.5 - Prob. 68E Ch. 8.5 - Prob. 69E Ch. 8.5 - Prob. 70E Ch. 8.5 - Prob. 71E Ch. 8.5 - Prob. 72E Ch. 8.5 - Prob. 73E Ch. 8.5 - Prob. 74E Ch. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE Ch. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Prob. 15RE Ch. 8 - A die is constructed in such a way that rolling a...Ch. 8 - Prob. 17RE Ch. 8 - Prob. 18RE Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Prob. 23RE Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - In Exercises 2934 the mean and standard deviation...Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 1CS Ch. 8 - Prob. 2CS Ch. 8 - Prob. 3CS Ch. 8 - Prob. 4CS Ch. 8 - Which of the following lists of data would you...Ch. 8 - Prob. 6CS Ch. 8 - Prob. 7CS Ch. 8 - Prob. 8CS

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The approximate probability such that Goode will do at least well where 49 % prefer Goode in a political poll, where the probability that each person will tell his or her preference is 90 % . Total number of persons polled are 1000 out of which 51 % prefer candidate Goode and 49 % prefer Slick.

Solution Summary: The author calculates the approximate probability such that Goode will do at least well in a political poll, where the probability that each person will tell their preference is 90%.

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