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Normal distribution: Definition, Word Problems, Videos

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Contents:
What is a Normal distribution?
Normal Distribution Articles
Normal Distribution Word Problems


What is a Normal distribution?


IQ scores fit a bell curve shape.

IQ scores fit a bell curve shape.




Data can be spread out in a variety of ways. Normal distribution refers to a distribution shaped like a bell curve. the data tends to cluster around the center of the distribution, with fewer data points at the ends. It’s widely used because many naturally occurring phenomena tend to be shaped like this particular distribution, including heights, weights, and test scores (for example, the SAT).
A normal distribution has the following characteristics:

  • The mean, mode and median are all equal.
  • The curve is symmetric at the center.
  • Exactly half of the values are to the left of center and exactly half the values are to the right.

Read the full normal distribution definition at: What is a Normal Distribution?


Normal Distribution Articles


You’ll find dozens of articles on this site for every aspect of the normal distribution. These are some of the most popular. You can find more normal distribution articles at the Normal Distributions page. Don’t see what you are looking for? Type a search term into the search boxes at the top or in the right-hand sidebar. Or hop over to our YouTube channel for videos.

  1. What is the 68-95-99.7 Rule?
  2. What is Normal Distribution Probability?
  3. How to Calculate a Z-Score in Statistics
  4. What is a Z-Table?
  5. Area Under a Normal Distribution Curve Index


Normal distribution Word Problems


When you tackle normal distribution in a statistics class, you’re trying to find the area under the curve. The total area is 100% (as a decimal, that’s 1). Normal distribution problems come in six basic types. How do you know that a word problem involves normal distribution? Look for the key phrase “assume the variable is normally distributed” or “assume the variable is approximately normal.” To solve a normal distribution word problem you need to figure out which type you have. You can do this in three easy steps:

Step 1: Read the problem and identify the pieces of information you are given: for example, you might be given the mean, the standard deviation and the number of randomly selected items.

Step 2: Find the items you identified in step 1 in the second column in the table (the column titled “GIVEN”).

Step 3: Check the third column for what the problem is asking you to do. Then follow the link in the first column for a step-by-step article.

Post Given Asked to find…
Normal Distribution word problems less than (click here).
  1. mean (average or μ)
  2. standard deviation (σ)
  3. number selected (i.e. “choose one at random” or “select ten at random”)
The size or probability of “less than” or “fewer than” or “under” a certain amount (i.e. “under $5,000″)
Statistics Normal distribution word problems Above (click here).
  1. mean (average or μ)
  2. standard deviation (σ)
  3. number selected (i.e. “choose one at random” or “select ten at random”)
The size or probability of “more than” or “greater than” or “over” a certain amount (i.e. “under $5,000″)
Word problems with normal distribution: Between (click here).
  1. mean (average or μ)
  2. standard deviation (σ)
  3. number selected (i.e. “choose one at random” or “select ten at random”)
The size or probability of “in between”  (i.e. “in between $5,000 and $10,000″)
Normal distribution word problems with solutions: finding Middle percentage (click here).
  1. the mean (average or μ)
  2. standard deviation (σ)
  3. the “middle percentage” amount (i.e 50%, 70% etc.)
Find the upper and lower limits for a certain given middle percentage
Normal distribution word problems and answers: lower cut off (click here).
  1. the mean (average or μ)
  2. standard deviation (σ)
  3. the “upper percentage” amount (i.e 10%, 30% etc.)
find the lower cut off point, given an upper percentage
Normal distribution word problems finding an upper cut off point (click here).
  1. the mean (average or μ)
  2. standard deviation (σ)
  3. the “upper percentage” amount (i.e 10%, 30% etc.)
find the upper cut off point, given a lower percentage

17 thoughts on “Normal distribution: Definition, Word Problems, Videos

  1. Lida Cako

    What is the difference between class limit and class boundaries in frequency tables? Class limit is explained in text, but there’s no mentioning of class boundaries (unless I missed it)
    Thank you,
    Lida

  2. Rebecca Gamble

    I used to find word problems to be hard, is can be hard to find out what the problem is asking you to do. You find yourself spending more time studying the question and if you’re like me over analysis and use the wrong formula or worst just guess. I know I’m going to use this technique on our next exam.

  3. Mark McCrea

    I know. I am doing the samething trying see what formula I am needing to use in the case.

  4. Lisa Barcomb

    Word problems to me are just hard. I don’t know why I can’t get them but I wish the light would come on in my head so I would not have such a hard time doing them. Because I really like this class it just seems like its getting the best of me.

  5. Jennifer Thomas

    I just came across this index. This would have been helfpul to me. I too had trouble trying to understand the word problem and determining which method I should use.

  6. angie widdows

    Even with this example, I am still very confused on this one. More than, Less than, I think I need to look at the example again.

  7. Angella Clarke

    I think that the hardest part about word problems for me is trying to figure out what the question is really asking.

  8. Vanessa DuBarry

    i agree. i never know exactly what they want me to do or what formula to use. even though this blog is helpful but it is still a little overwhelming.

  9. Sunita Sharma

    Iam so happy by getting to learn fron internet. thank you
    show more problem and solution so that we can learn more……