At a certain university, the mean age is 20, the standard deviation is 2.7, and the ages are positively skewed. a. If a person is randomly selected from the university, what is the probability of getting a person younger than 25? (Show as much work as possible. Round the z score to two decimal places. Leave your final answer with four decimal places) b. What percentage of the university is younger than 25? (No need to show work. Leave your final answer with two decimal places) c. draw a diagram (Draw a sketch of a normal distribution. Under the normal distribution, include a number line with a tick mark that is labelled with both the mean of the population and z = 0. This tick mark needs to be at the center of the normal distribution. Also, include another tick mark showing the age you converted to a z score and the z score of that age. This tick mark doesn't need to be perfectly positioned but it needs to

be positioned at least roughly the correct location. Remember that almost all of the normal distribution is between z = -3 and z = +3. This should help you determine the position of your z score. Finally, shade the area that corresponds to the probability you calculated in this problem, and label the shaded area with both the probability and the percentage (from parts a and b of this problem).

8. What is the mean absolute deviation (MAD) of 10, 30, 50, and 70? (Show as much work as possible) 9. In a population of 4 people, the ages are 10, 30, 50, and 70. What are the variance and standard deviation of the population? (Show as much work as possible. Round each answer to two decimal places) 10. In a sample of 4 people, the ages are 10, 30, 50, and 70. What are the variance and standard deviation of the sample? (Show as much work as possible. Round each answer to two decimal place