samatha is a leading traveling nurse.samatha is presently researching the number of patients treated per hour.samtha develops the following probability distribution.

Number of patients treated per hour	Probability
3	0.4
6	0.3
10	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 treated per hour?

c) What is the mean (expected value) for the number of patients treated per hour?

d) If a sample of size 15 is taken, what is the expected value of the sample mean?

e) If a sample of size 15 is taken, what is the probability the sample mean is greater than 9.5?

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 9.5?

i) If a sample of size 36 is taken, what is the standard error of the mean?

2) lori is leading psychologist. lori is presently researching the relationship between stress and cardiovascular disease.Suppose systolic blood pressures of patients that are experiencing chronic stress is normally distributed with a mean of 140 and a standard deviation of 5.9.

a) In a random sample of 16 chronically stressed patients, what is the probability the sample mean is less than 132? Would you classify this observation as an outlier?Why or why not?

b) What is the probability a randomly selected chronically stressed patient has a systolic blood pressure less than 132? Would you classify this observation as an outlier? Why or why not?

c) What is the Interquartile Range (IQR) for systolic blood pressures for chronically stressed patients?

d) If you took a random sample from this population and constructed a box-and-whisker plot, approximately what would be the three values on the box?

e) One patient's systolic blood pressure was 2.05 standard deviations above the mean. What was this patient's systolic blood pressure?

f) Using Z > 2 as a criterion for an outlier, what is the minimum sample size such that a sample mean of 143 would be classified as an outlier?

g) jies is developing new techniques with the goal of decreasing systolic blood pressures. jies desires the population mean to be such that in a random sample of 9 patients the probability the sample mean is less than 133 is 0.85 (assume the population standard deviation = 5.9). In order to accomplish jies goals, the population mean can be no more than ___ (round your answer to 2 decimal places)?