Potassium Requirement. The normal daily potassium requirement for humans falls within the range of 2,000 to 6,000 milligrams (mg), with larger amounts needed during the hot summer months. The potassium content in different foods varies, but measurements indicate that bananas contain a high level of potassium, with approximately 422 mg in a medium-sized banana. Suppose the distribution of potassium in bananas is normally distributed, with a mean equal to 422 mg and a standard deviation of 13 mg per banana. You consume milligrams of potassium from them.n = 3 bananas per day, and T is the total number of milligrams of potassium you receive from them.a. Find the mean and standard deviation of T.b. Find the probability that your daily potassium intake from the three bananas exceeds 1,300 mg. (Hint: Note that T is the sum of three random variables X1, X2, and X3, where X1 is the amount of potassium in banana 1, etc.)

Given information: Let X be the potassium in bananas is normally distributed, with a mean equal to…

Answered: Potassium Requirement. The normal daily…

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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Potassium Requirement. The normal daily potassium requirement for humans falls within the range of 2,000 to 6,000 milligrams (mg), with larger amounts needed during the hot summer months. The potassium content in different foods varies, but measurements indicate that bananas contain a high level of potassium, with approximately 422 mg in a medium-sized banana. Suppose the distribution of potassium in bananas is normally distributed, with a mean equal to 422 mg and a standard deviation of 13 mg per banana. You consume milligrams of potassium from them.

n = 3 bananas per day, and T is the total number of milligrams of potassium you receive from them.

a. Find the mean and standard deviation of T.

b. Find the probability that your daily potassium intake from the three bananas exceeds 1,300 mg. (Hint: Note that T is the sum of three random variables X1, X2, and X3, where X1 is the amount of potassium in banana 1, etc.)

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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