Question

# Consider two normal distributions, one with mean-4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false

Normal distributions
Consider two normal distributions, one with mean-4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false to each statement and explain your answers.
a. The two normal distributions have the same spread.
b. The two normal distributions are centered at the same place.

2021-02-27
Step 1
(a)
The spread is represented by standard deviation. If the standard deviations of the two or more normal distributions are same then the spread of the two or more normal distributions is same.
Here, it is observed that the standard deviations of the two normal distributions are same. Thus, it can be concluded that the spread of the two normal distributions is same.
Hence, the given statement is true.
Step 2
(b)
The parameter mean affects where the normal curve is centered. If the mean of the normal distributions are different, then the normal curve is centered at a different place.
Here, it is observed that the mean of the two normal distributions are different then the normal curve is centered at a different place.
Hence, the given statement is false.