A random sample of n=36 scores is selected from a population. Will this have a definite normal distribution?
It is likely but not certain.
No, a random sample of 36 scores from a population does not guarantee a definite normal distribution. The distribution of the sample will be approximately normal if the population from which it is drawn is normal or if the sample size is sufficiently large (according to the Central Limit Theorem). However, if the population is not normal and the sample size is small, the sample distribution may not be exactly normal.
To determine whether a random sample will have a definite normal distribution, you can use the Central Limit Theorem (CLT). The CLT states that as sample size increases, the distribution of sample means will become approximately normal, regardless of the shape of the population distribution, as long as the sample size is sufficiently large.
According to the CLT, if the sample size is large enough (typically n > 30), the sample means will be approximately normally distributed. In your case, since the sample size is n=36, it meets the requirement for a large sample size, and thus, the sample means will be approximately normally distributed.
However, it is worth noting that the population from which the sample is selected does not need to be normally distributed for the sample means to be approximately normally distributed. The CLT applies regardless of the population's distribution shape.
Therefore, while the sample itself may not have a definite normal distribution, the sample means will be approximately normally distributed due to the Central Limit Theorem.