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Chapter 6: Q.10 (page 385)

Is X~N(0,1) a standardized normal distribution? Why or why not?

Short Answer

Expert verified

It is clear that X follows standard deviation distribution because its mean is zero and the standard deviation is 1.

Hence, X~N(0,1) is a standard normal distribution.

Step by step solution

01

Given Information

Given the value that, X~N(0,1)

02

Explanation

If a normal distribution is standardized then normal distribution will evolve standard normal distribution and then it can be defined as below:

Z~N(0,1)

Where,

渭=0

蟽=1

It is given that X follows normal distribution such that,

X~N(0,1)

So, it is clear that X follows standard deviation distribution because its mean is zero and the standard deviation is 1.

Hence, X~N(0,1) is standard normal distribution.

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Most popular questions from this chapter

Suppose that Ricardo and Anita attend different colleges. Ricardo's GPA is the same as the average GPA at his school. Anita's GPA is 0.70 standard deviations above her school average. In complete sentences, explain why each of the following statements may be false.

a. Ricardo's actual GPA is lower than Anita's actual GPA.

b. Ricardo is not passing because his z-score is zero.

c. Anita is in the 70th percentile of students at her college.

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Suppose X has a normal distribution with mean 25 and standard deviation of five. Between what values of x do 68% of the values lie

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