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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Butterfat A quart of Parker's milk contains a mean of 39 g of butterfat, with a standard deviation of 2 g. If the butterfat is normally distributed, find the probability that a quart of this brand of milk chosen at random will contain between

(a) 39 and 43 g of butterfat.

(b) 36 and 39 g of butterfat.

(a)

To determine

To calculate: The probability that a quart of this brand of milk will contain between 39 and 43 g butterfat and chosen at random using standard normal distribution if a quart of Parker’s milk contains a mean of 39 g of butterfat with a standard deviation of 2 g.

Explanation

Given Information:

A quart of brand of milk chosen at random will contain between 39 and 43 g, so the probability is Pr(39x43), the mean is 39 g and a standard deviation of 2 g.

Formula used:

If data for a population are normally distributed, the z score is,

z=xμσ

Where σ is the standard deviation of the population data, x is the number of standard deviation and μ is mean.

Calculation:

Consider the provided probability is Pr(39x43),

The mean and standard deviation is;

μ=39 and σ=2

To find the value of provided probability use the formula z=xμσ

(b)

To determine

To calculate: The probability that a quart of this brand of milk chosen at random will contain between 36 and 39 g of butterfat using standard normal distribution if a quart of Parker’s milk contains a mean of 39 g with a standard deviation of 2 g.

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