Answered: (a) Give the numerical value of the…

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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Question

Suppose the probability is p = 0.36 that a person who purchases an instant lottery ticket wins money, and this probability holds for every ticket purchased. Consider different random samples of n = 64 purchased tickets. Let p̂ = sample proportion of winning tickets in a sample of 64 tickets.

(a) Give the numerical value of the mean of the sampling distribution of p̂. (Round your answer to two decimal places.)
Mean =

(b) Calculate the standard deviation, s.d. of the sampling distribution of p̂. (Round your answer to two decimal places.)
s.d.(p̂) =

(c) Use the Empirical Rule to find values that fill in the blanks in the following sentence. (Round your answers to two decimal places.)

In about 68% of all randomly selected samples of n = 64 instant lottery tickets, the proportion of tickets that will be money winners will be between and .

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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