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A normal distribution has a mean of µ = 28 with σ = 5. Find the...

A normal distribution has a mean of µ = 28 with σ = 5. Find the scores associated with the following regions:

a. the score needed to be in the top 41% of the distribution b. the score needed to be in the top 72% of the distribution c. the scores that mark off the middle 60% of the distribution

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Expert Solution

Solution: We are given:

a. the score needed to be in the top 41% of the distribution

Answer: Top 41% will have 59% of scores below it. Therefore, we will first find the z value corresponding to probability 0.59. Using the standard normal table, we have:

Therefore, we have:

Therefore, the score needed to be in the top 41% of the distribution is

b. the score needed to be in the top 72% of the distribution.

Answer: Top 72% will have 28% of scores below it. Therefore, we will first find the z value corresponding to probability 0.28. Using the standard normal table, we have:

Therefore, we have:

Therefore, the score needed to be in the top 72% of the distribution is

c. the scores that mark off the middle 60% of the distribution.

Answer: The middle 60% of the scores will have 20% of scores below it and 20% of scores above it. First let's find the z value corresponding to probability 0.20. Therefore, using the standard normal distribution, we have:

Therefore, we have:

Now to find z value of the 20% above the middle 60%, we will find the z value corresponding to probability 0.80 because 80% of scores lies below the top 20% of scores. Using the standard normal table, we have:

Therefore, we have:

Therefore, the scores that mark off the middle 60% of the distribution is and

milcah answered 6 days ago

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