Answer true or false to each statement. Explain your answers. a. Two normal distributions that have the same mean are centered at the same place, rega

Question

Answer true or false to each statement. Explain your answers.
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.

Answer 1

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.

Answer true or false to each statement. Explain your answers. a. Two normal distributions that have the same mean are centered at the same place, rega

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