Question 1162044: Suppose a population is normally distributed with a mean 100 and a standard deviation of 15. When a sample of size n = 36 is collected a sampling distribution is created. Explain which is larger: the probability of a value randomly selected from the population being larger than 120, or the probability of a sample mean being larger than 120.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The probability of a single item selected from the population being greater than 120 is significantly larger than the sample mean of 36 items being larger than 120. Aside from the mathematics involved, intuitively, one would expect it to be more difficult for an average of 36 items to be more than 120, since while some would be, many others would be less than and would have to be counterbalanced.
z>(20/15) or 4/3 for the first, which is around 10% probability.
z> 120/15 or 8 for the second, which is essentially 0 probability
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