Please type everything out and show your work. Thank you very much!!!!!

1) (50 points) In the year 2032, Mari Alba-Rodriguez is a leading pediatric psychiatrist. Mari is is presently researching the number of patients seen per day. Mari develops the following probability distribution. Number of projects per year Probability 2 0.4 7 0.3 0.2 12 0.1 a) What shape is the above probability distribution (symmetric, positively skewed, negatively skewed)? b) What is the standard deviation for the number of patients seen per day? c) What is the mean (expected value) for the number of patients seen per day? d) If a sample of size 15 is taken, what is the expected value of the sample mean? ) If a sample of size 15 is taken, what is the probability the sample mean is greater than 8.5? f) If a sample of size 15 is taken, what is the standard error of the mean? g) If a sample of size 36 is taken, what is the expected value of the sample mean? h) If a sample of size 36 is taken, what is the probability the sample mean is greater than 8.5? i) If a sample of size 36 is taken, what is the standard error of the mean