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Suppose a population has a mean of 400 and a standard deviation of 24. if a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean of more than 404.5 is:

Respuesta :

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Find the critical value or test statistic.
[tex]z = \frac{m - \mu}{\sigma/\sqrt{n}} = \frac{404.5 - 400}{24/\sqrt{144}} = \frac{4.5}{2} = 2.25[/tex]

Find P(z > 2.25) using a normal distribution table

P(z > 2.25) = 0.0122

The probability of drawing a sample with a mean of more than 404.5 is: 0.0122

How to find the p-value?

We are given;

Population Mean; μ = 400

Standard Deviation; σ = 24

Sample Size; n = 144

Sample mean; x' = 404.5

Formula for z-score is;

z = (x' - μ)/(σ/√n)

z = (404.5 - 400)/(24/√144)

z = 2.25

From online p-value from z-score calculator, we have;

p-value = 0.0122

Read more about p-value at; https://brainly.com/question/4621112

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