Research shows that 70% of US citizens have been to Disney World. Suppose we are constructing a sampling distribution for the proportion of US citizens who have been to Disney World, using all possible samples of size 300. (a) What is the mean of this distribution? Round your answer to 2 decimal places.(b) What is the value of the proportion of failures in this distribution? Round your answer to 2 decimal places. (c) What is the standard deviation of this distribution? Round your answer to 3 decimal places. (d) What is the expected number of successes? (e) What is the expected number of failures? (f) What is the probability of selecting a sample with the proportion of citizens who have visited Disney World being 0.67 or lower? Round your answer to three decimals.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Research shows that 70% of US citizens have been to Disney World.

Suppose we are constructing a sampling distribution for the proportion of US citizens who have been to Disney World, using all possible samples of size 300.

(a) What is the mean of this distribution? Round your answer to 2 decimal places.

(b) What is the value of the proportion of failures in this distribution? Round your answer to 2 decimal places.

(c) What is the standard deviation of this distribution? Round your answer to 3 decimal places.

(d) What is the expected number of successes?

(e) What is the expected number of failures?

(f) What is the probability of selecting a sample with the proportion of citizens who have visited Disney World being 0.67 or lower? Round your answer to three decimals.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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