State the three conclusions of the Central Limit Theorem: . . . 3. If we are given a random variable X~ N(µ,o), then the distribution of sample means(of sample size n) is described symbolically by:_______________________ 4. Multiple choice: As the sample size n increases, the distribution of sample means: a. Becomes narrower b. Remains constant c. Becomes wider 5. Multiple choice: According to the Central Limit Theorem, the mean of the sample means is: a. Less than the population mean b. The same as the population mean c. More than the population mean 6. Multiple choice: According to the Central Limit Theorem, the standard deviation of the sample means is: a. Less than the population standard deviation b. The same as the population standard deviation c. More than the population standard deviation we can assume the distribution of 7. In practice, if the sample size n is at least sample means is normal. 8. An unknown distribution has a mean of 45 and a standard deviation of 8. Samples of size n = 30 are drawn randomly from the population. a. Find the probability that the sample mean is between 42 and 50. Write the calculator function as well as what has been entered and round your answer to 3 decimal places. b. Find the value of X that is two standard deviations above the expected value, 45, of the sample mean. 9. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours. 10. The mean number of minutes for app engagement by a tablet user is 8.2 minutes.Suppose the standard deviation is one minute. Take a sample of 60. a. What is the mean for the sample mean number of app engagement by a tablet user? b. What is the standard error of the mean? c. Find the 90th percentile for the sample mean time for app engagement for a tablet user. Interpret this value in a complete sentence. d. Find the probability that the sample mean is between eight minutes and 8.5 minutes.

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State the three conclusions of the Central Limit Theorem: . . . 3. If we are given a random variable X~ N(µ,o), then the distribution of sample means(of sample size n) is described symbolically by:_______________________ 4. Multiple choice: As the sample size n increases, the distribution of sample means: a. Becomes