Q. 8 - Elementary Statistics

Question

Answer true or false to each statement. Give reasons for your answers.

a. Two variables that have the same mean and standard deviation have the same distribution.

b. Two normally distributed variables that have the same mean and standard deviation have the some distribution.

Step-by-Step Solution

Answer

a. The other parameters mean and standard deviation may differ. The type of the distribution is not specified.

This given statement is false. 

b. The two normally distributed variables with same mean and standard deviation have the same shape.  This given statement is true. 

Part (a) Step 1: Given Information

Two variables that have the same mean and standard deviation have the same distribution. whether the given statement is true or false.

Part (a) Step 2: Explanation

Consider "two variables with same mean and standard deviation have the same distribution.

The shape of the distribution depends on their parameters.

So the other parameters mean and standard deviation may differ. 

The type of the distribution is not specified.

Hence, the given statement is false.

Part (b) Step 1: Given Information

Two normally distributed variables that have the same mean and standard deviation have the some distribution. Whether the given statement is true or false.  

Part (b) Step 2: Explanation

Consider "two normally distributed variables with same mean and standard deviation have the same distribution.

The mean and standard deviation determine the normally distributed.

So, two normally distributed variables with same mean and standard deviation have the same shape. 

Hence, the given statement is true.