Mathematics: Amachine fills containers with a particular product. the standard deviation of filling weights is known from past data to be .6 ounce. if only 2% of the containers hold less than 18 ounces, what is the mean filling weight for the machine? that is, what must m equal? assume the filling weights have a normal distribution. anderson, david r.. essentials of statistics for business and economics (p. 299). south-western college pub. kindle edition.

Amachine fills containers with a particular product.

Chris5181

06.01.2022

The mean of weight is 30.3

Step-by-step explanation:

We are given the following information in the question:

Standard Deviation, σ = 6 ounces

We are given that the weights is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(container holds less than 18 ounces) = 2% = 0.02

P(x < 18) = 0.02

$P( x < 18) = P( z < \displaystyle\frac{18 - \mu}{6}) = 0.02$

Calculation the value from standard normal z table, we have,

P(Z < -2.05) = 0.02

$\displaystyle\frac{18 - \mu}{6} = -2.05\\\\\mu =18- (6\times -2.05) = 30.3$

Hence, the mean of weight is 30.3

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Jaylanbeadles

10.03.2020

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Step-by-step explanation:

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