Normal Distribution: Solution For The Word Problems

In our previous articles we have seen how to solve the Normal Distribution problems by using the Empirical Rule Formula. In this article, we will be studying about how to solve the word problems with examples.

When you are trying to solve the normal distribution in the statistics class, you will be trying to find the area below the curve. The total area below the curve will be 100%, i.e. as the decimal it will be 1. There are six fundamental categories of the Normal Distribution problems. How will you determine that in the word problem the normal distribution is involved? You need to check the phrase, “assume the variable is approximately normally distributed”. You must be wondering that what is meaning of this phrase. You need to determine the type you have with you.

Word Problems With The Normal Distribution

• Between
  • Detect the word problem elements.
    • Compute the mean (µ)
    • Compute the Standard Deviation (σ)
    • Select the number, i.e. “one randomly” or “ten randomly”
    • X: the numbers related with “Between”, i.e. $5,000 and $10,000, the value of X is as 5,000 and 10,000

Besides you might get EITHER

1. Sample size
2. Compute the probability
   • Now, draw the graph, by using the mean computed in the previous step. Plot the numbers which are associated with “BETWEEN”. Your graph will look like
   • Now compute the Z-Scores. Now substitute the value of X in the Z equation as shown below. The value of µ will be 100 as shown in the graph.

Z = (x – µ) / σ

• Repeat the third step for the second value of X.
• The values which you will get from the 3^rd and 4^th step, now you can calculate the area in the Z-table.

If in the question you have been asked to find the probability also then carry on with the 6^th step as below.

• Now, convert the values from the 5^th step into the percentage.

Example, 0.1293 is 12.93%

• Now, multiply the value which you have computed in the 1^st step with the Z-value in the step 4^th.
• “More Than” / “Above”
  • Break these words into and then compute
    • mean (µ)
    • Standard Deviation (σ)
    • and then pick a number, i.e. “one randomly” or “ten randomly”
    • X: the numbers related with “less than”, if you are asked to find the value below $9,999 then the X will be 9,999
  • Now, calculate the sample value from the problem given. You may have a certain size or the general sample.

Draw the graph as shown below

• Now compute the Z-Scores. Now substitute the value of X in the Z equation as shown below. The value of µ will be 100 as shown in the graph.

Z = (x – µ) / σ

• With the values which you will get from the 3^rd and 4^th step, now you can calculate the area in the Z-table.
• Now, convert the values from the 5^th step into the percentage.
• Now, multiply the value which you have computed in the 1^st step with the Z-value in the step 4^th.

Conclusion: In this article we have seen that what is Word Problems in the Normal Distribution and how to solve the word problems. In our further related topics we will see more examples.