Answer true or false to each statement. a. Two normal distributions that have the same mean are centered at the same place, regardless of the relation

amanf 2020-11-22 Answered
Answer true or false to each statement.
a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.
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Expert Answer

broliY
Answered 2020-11-23 Author has 97 answers
Step 1
The mean represents the average and it determines the centre of the distribution and the standard deviation represents the spread of the distribution.
Step 2
a)
Here, it is observed that the mean determines the center of the distribution. Thus, it can be concluded that two normal distributions having the same mean are centered at the same place. Thus, the given statement is true.
b)
Here, it is observed that the standard deviation determines the spread of the distribution. Thus, it can be concluded that two normal distributions that have the same standard deviation have the same spread. Thus, the given statement is true.
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