Distribution of sample meansa and b Suppose the daily attendance at Disneyland is normally distributed with mean 52(thousand) and standard deviation 8.4 (thousand), and we take a random sample of15 days in a typical year and their daily attendance.a. Check the necessary assumptions and conditions for using the Normal Modelfor your sampling distribution.b. What are the mean and standard deviation for the sampling distribution ofsample mean?c. What is the probability that the sample mean will be less than 55 (thousand)?d. What is the probability that the sample mean will be greater than 50(thousand)?e. What is the probability that the sample mean will be between 49 (thousand)and 55 (thousand)?

Given Information: Daily attendance at Disneyland is normally distributed with mean 52 and standard…

Answered: Distribution of sample means a and b

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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Distribution of sample means

a and b

Suppose the daily attendance at Disneyland is normally distributed with mean 52
(thousand) and standard deviation 8.4 (thousand), and we take a random sample of
15 days in a typical year and their daily attendance.
a. Check the necessary assumptions and conditions for using the Normal Model
for your sampling distribution.
b. What are the mean and standard deviation for the sampling distribution of
sample mean?
c. What is the probability that the sample mean will be less than 55 (thousand)?
d. What is the probability that the sample mean will be greater than 50
(thousand)?
e. What is the probability that the sample mean will be between 49 (thousand)
and 55 (thousand)?

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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