Answered: ) What is the probability that a single…

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 1:

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=542.9 and standard deviation σ=28.4.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 547 or higher?
ANSWER: ____________

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯, of 35 students?
The mean of the sampling distribution for x¯is: __________
The standard deviation of the sampling distribution for x¯ is: ___________

(d) What is the probability that the mean score x¯ of these students is 547 or higher?
ANSWER: _____________

Question 2:

The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.7 ounces and standard deviation 0.17 ounces.

(a) What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with four of these chocolate bars is between 7.59 and 7.87 ounces?
ANSWER: ________

(b) For a SRS of four of these chocolate bars, what is the level LL such that there is a 3% chance that the average weight is less than LL?
ANSWER: ____________

Question 3

A die is continuously rolled until the total sum of all rolls exceeds 325. What is the probability that at least 95 rolls are necessary? _____________

Question 4:

Given a normal population whose mean is 665 and whose standard deviation is 24, find each of the following:

A. The probability that a random sample of 3 has a mean between 667 and 673.
Probability = _________

B. The probability that a random sample of 15 has a mean between 667 and 673.
Probability = _________

C. The probability that a random sample of 27 has a mean between 667 and 673.
Probability = ___________

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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