If the population is normally distribution then the sample must be normally distributed even for small sample size? True or False.
The variance of the standard normal distribution is always equal to 1.? True or False.
A continuous random variable may not be normally distributed? True or False.
False
False
True
If the population is normally distributed, then the sample is also expected to be normally distributed, even for small sample sizes. This is known as the Central Limit Theorem, which states that as sample size increases, the distribution of sample means becomes closer to a normal distribution.
The statement "The variance of the standard normal distribution is always equal to 1" is true. The standard normal distribution is a specific normal distribution with a mean of 0 and a variance of 1. Any random variable that follows this distribution is said to be standard normally distributed.
A continuous random variable may or may not be normally distributed. Normal distribution is just one of many possible distributions for continuous random variables. Other common distributions include uniform distribution, exponential distribution, and beta distribution, to name a few. The shape of the distribution depends on the specific characteristics of the variable and does not have to conform to the normal distribution. Therefore, the statement "A continuous random variable may not be normally distributed" is true.