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Normal/standard Distribution and Level of significance

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a) What is the difference between a normal distribution and a standard normal distribution?

b) What is the purpose of using a standard normal distribution instead of the normal distribution?

c) Please cite one example of how the standard normal distribution is used, including the Z-values for your example.

d) If you are given the level of significance, how do you obtain the critical value?

e) How are z-values related to hypothesis testing?

f) Describe the five-step hypothesis testing process?

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Solution Summary

The solution explains the difference between normal and standard distribution and how to obtain the critical value when given a certain level of significance. The five-step hypothesis testing process is described and explains how z-values are related to hypothesis testing.

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a) What is the difference between a normal distribution and a standard normal distribution?

For normal distribution, there are two parameters: mean µ and standard deviation σ. If µ=0 and σ=1, the corresponding normal distribution is called a standard normal distribution.

b) What is the purpose of using a standard normal distribution instead of the normal distribution?

When you are asked to find a probability involving a random ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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  • "Thank you very much for your valuable time and assistance!"
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