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A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 23.4 pounds and a standard deviation of 6.8 pounds.
Step 2 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 63 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

Respuesta :

Using the Central Limit Theorem, the standard deviation of the sampling distribution of sample means would be of 0.86.

What does the Central Limit Theorem state?

It states that the standard deviation of the sampling distribution of sample means is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In which:

  • [tex]\sigma[/tex] is the standard deviation of the population.
  • n is the sample size.

The parameters for this problem are given as follows:

[tex]\sigma = 6.8, n = 63[/tex].

Hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]s = \frac{6.8}{\sqrt{63}}[/tex]

s = 0.86.

More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444

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