Question

In: Statistics and Probability

1. The grades on a chemistry midterm at Springer are roughly symmetric with μ=67 and σ=2.0....

1. The grades on a chemistry midterm at Springer are roughly symmetric with μ=67 and σ=2.0. William scored 66 on the exam.

  1. Find the z-score for William's exam grade. Round to two decimal places.
  2. What percentage of students in this midterm scored less than William?
  3. What percentage of students scored more than 70 in this midterm?

2. The grades on a language midterm at Oak are roughly symmetric with μ=67 and σ=2.5. Ishaan scored 70 on the exam.

  1. Find the z-score for Ishaan's exam grade. Round to two decimal places.
  2. What percentage of students in this midterm scored less than Ishaan?
  3. What percentage of students scored more than 70 in this midterm?

3. The grades on a math midterm at Springer are roughly symmetric with μ=78 and σ=5.0. Omar scored 70 on the exam.

  1. Find the z-score for Omar's exam grade. Round to two decimal places.
  2. What percentage of students in this midterm scored less than Omar?
  3. What percentage of students scored more than 80 in this midterm?
  4. What percentage of students scored between 70 and 90 in this midterm?

4. The grades on a geometry midterm at Springer are roughly symmetric with μ=68 and σ=2.0. Emily scored 69 on the exam.

  1. Find the z-score for Emily's exam grade. Round to two decimal places.
  2. What percentage of students in this midterm scored less than Emily?
  3. What percentage of students scored more than 75 in this midterm?
  4. What percentage of students scored between 65 and 75 in this midterm?

Solutions

Expert Solution

Let us first clear about the term "roughly symmetric" in Normal distribution

is mean to follow the Law of "Area of Symmetricity"

i.e.

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(1.) Formula for finding Z- Scores :

Z - Scores of William's exam grade =

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  -----------------------------------------------------     

That means 19.15% students scored less than William .

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That means 6.68% students scored more than 70 .

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(2.) Z- Score of Ishaan :

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That means 38.49% students scored less than Ishaan .

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That means 11.51% students scored more than 70 .

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(3.) Z-scores of Omar :

      -----------------------------------------------------     

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That means 5.48% students less than Omar .

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That means 34.46% students scored more than 80 .

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  -----------------------------------------------------     

That means 4.66% students scored between 70 and 90.

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(4.) Z-Scores of Emily :

---------------------------------------------------------------------------------

That means 19.15% students scored less than Emily.

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That means 0.02% students scored more than 75.

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  -----------------------------------------------------     

That means 6.66% students scored between 65 and 75 .

__________________________________________________________________________________________________

orchestra answered 1 year ago
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