Problem #3: Please answer parts a and b. The weight of a sophisticated running shoe is normally distributed with a mean of 13 ounces.(a)What must the standard deviation of weight be in order for the company to state that 95% of its shoes weight less than 14 ounces?(b)Suppose that the standard deviation is actually 0.83. If we sample 8 such running shoes, find the probability that exactly 3 of those shoes weigh more than 14 ounces. Problem #3: The weight of a sophisticated running shoe is normally distributedwith a mean of 13 ounces.(a) What must the standard deviation of weight be in order for thecompany to state that 95% of its shoes weight less than 14ounces?(b) Suppose that the standard deviation is actually 0.83. If wesample 8 such running shoes, find the probability that exactly 3of those shoes weigh more than 14 ounces.

Given, Let X be the weight of a sophisticated running shoe. X is normally distributed. Mean (μ)=13…

Answered: Problem #3: Please answer parts a and…

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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Problem #3: Please answer parts a and b.

The weight of a sophisticated running shoe is normally distributed with a mean of 13 ounces.

(a)	What must the standard deviation of weight be in order for the company to state that 95% of its shoes weight less than 14 ounces?

(b)	Suppose that the standard deviation is actually 0.83. If we sample 8 such running shoes, find the probability that exactly 3 of those shoes weigh more than 14 ounces.

Problem #3: The weight of a sophisticated running shoe is normally distributed
with a mean of 13 ounces.
(a) What must the standard deviation of weight be in order for the
company to state that 95% of its shoes weight less than 14
ounces?
(b) Suppose that the standard deviation is actually 0.83. If we
sample 8 such running shoes, find the probability that exactly 3
of those shoes weigh more than 14 ounces.

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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