I need help with these math questions. They revolve around the Central Limit Theoram?
1. Does this mean that problems involving sampling distributions can be solved in the exact same manner as ordinary z-score area problems, except that we use a new (and smaller) standard deviation?
2. Which is greater (in absolute value), the z-score of a data point x, or the z-score of a sample whose mean is x? (They are only the same if x equals the mean of the distribution, in which case each would have a z-score of 0.)
3. Suppose that a sampling distribution with n = 200 has a standard deviation of 1.6. How big would n have to be in order for the sampling distribution of size n from the same population to have a standard deviation of 0.8?
4. The length of human pregnancies is approximately normally distributed, with mean = 266 days and standard deviation = 16 days.
What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 or fewer days?
5. Old Faithful in Yellowstone National Park has a mean time between eruptions of 85 minutes, with a standard deviation of 21 minutes. What is the probability that a random sample of 30 time intervals between eruptions has a mean longer than 90 minutes? (Express your answer as a probability with two decimal places.)
6. Assume that the average withdrawal from an ATM is $67, with a standard deviation of $35. If a random sample of 50 ATM withdrawals is obtained, what is the probability that the average withdrawal is between $70 and $75?
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