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The weight of a loaf of bakery bread at the grocery store follows a Normal distribution with a mean of μ = 12 ounces and a standard deviation of σ = 1 ounce. Suppose we pick four loaves at random from the bin and find their total weight, W. Which of the following statements describes the random variable W?

The random variable W is binomial, with a mean of 48 ounces and a standard deviation of two ounces.
The random variable W is binomial, with a mean of 12 ounces and a standard deviation of two ounces.
The random variable W is Normal, with a mean of 12 ounces and a standard deviation of one ounce.
The random variable W is Normal, with a mean of 48 ounces and a standard deviation of two ounces.
The random variable W is Normal, with a mean of 48 ounces and a standard deviation of four ounces.

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Answer:

The random variable W is Normal, with a mean of 48 ounces and a standard deviation of four ounces.

Explanation:

By their properties, mean of μ(4x) = 4 * μ(x) and a standard deviation of σ(4x) = 4 * σ(x).

So the distribution of weight of four loaves of bread, W, still follows a Normal Distribution with a mean of 4*12 = 48 ounces and a standard deviation of 4*1 = 4 ounces.

lhmarianateixeira

The following statements describes the random variable W is Normal, with a mean of 48 ounces and a standard deviation of four ounces.

Given the information that:

  • distribution with a mean of μ = 12 ounces
  • standard deviation of σ = 1 ounce.
  • pick four loaves at random

By their properties, we have:

[tex]\mu(4x) = 4 * \mu(x) \\\sigma(4x) = 4 * \sigma(x).[/tex]

So the distribution of weight of four loaves of bread, W, still follows a Normal Distribution with a mean:

[tex]4*12 = 48 \\4*1 = 4[/tex]

See more about distribution at brainly.com/question/14926605

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