Let's analyze and understand the notation [tex]\( X \sim N(25, 31) \)[/tex].
The notation [tex]\( X \sim N(25, 31) \)[/tex] describes a normal distribution where:
- [tex]\( N \)[/tex] denotes that we are dealing with a normal distribution.
- The first parameter (25) represents the mean (or average) of the distribution.
- The second parameter (31) represents the standard deviation of the distribution.
Now let’s evaluate each of the given statements:
1. This is a binomial distribution:
- The notation [tex]\( X \sim N \)[/tex] specifically indicates a normal distribution, not a binomial distribution. So, this statement is false.
2. The standard deviation is 25:
- According to the notation [tex]\( X \sim N(25, 31) \)[/tex], the standard deviation is 31, not 25. Thus, this statement is false.
3. The variable is approximately normally distributed:
- The notation [tex]\( X \sim N \)[/tex] indeed indicates that the variable [tex]\( X \)[/tex] is normally distributed. Therefore, this statement is true.
4. The mean is 31:
- In the notation [tex]\( X \sim N(25, 31) \)[/tex], the mean is given as 25, not 31. Hence, this statement is false.
5. The mean is 25:
- The notation [tex]\( X \sim N(25, 31) \)[/tex] specifies that the mean of the normal distribution is 25. Therefore, this statement is true.
6. The standard deviation is 31:
- As indicated in [tex]\( X \sim N(25, 31) \)[/tex], the standard deviation is indeed 31. Thus, this statement is true.
Based on the analysis, the correct statements are:
- The variable is approximately normally distributed.
- The mean is 25.
- The standard deviation is 31.
So, if we consider the indices for these true statements, the correct options are:
- Statement 3: The variable is approximately normally distributed.
- Statement 5: The mean is 25.
- Statement 6: The standard deviation is 31.
Thus, the final answer is:
[tex]\[ [3, 5, 6] \][/tex]
