Riversongirlidn
Answered

IDNLearn.com makes it easy to find answers and share knowledge with others. Discover comprehensive answers to your questions from our community of experienced professionals.

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.

Sagot :

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.

Lhmarianateixeiraidn

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

We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is your go-to source for dependable answers. Thank you for visiting, and we hope to assist you again.