A manufacturer knows that their items have a normally distributed length, with a mean of 12.3 inches, and standard deviation of 3.2 inches.If one item is chosen at random, what is the probability that it is less than 13 inches long?___________A manufacturer knows that their items lifespans are normally distributed with mean = 5.6 and standard deviation = 0.8.What proportion of the items' lifespans will be longer than 8 years?___________________ Round to 4 decimal places.A particular fruit's weights are normally distributed, with a mean of 488 grams and a standard deviation of 11 grams.If you pick one fruit at random, what is the probability that it will weigh between 464 grams and 472 grams_____________

Let's assume, X = item's length The probability that the item is less than 13 inches long, is…

Answered: A manufacturer knows that their items…

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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A manufacturer knows that their items have a normally distributed length, with a mean of 12.3 inches, and standard deviation of 3.2 inches.

If one item is chosen at random, what is the probability that it is less than 13 inches long?___________
A manufacturer knows that their items lifespans are normally distributed with mean = 5.6 and standard deviation = 0.8.

What proportion of the items' lifespans will be longer than 8 years?

___________________ Round to 4 decimal places.
A particular fruit's weights are normally distributed, with a mean of 488 grams and a standard deviation of 11 grams.

If you pick one fruit at random, what is the probability that it will weigh between 464 grams and 472 grams_____________

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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