I have two probablity problems I'm stuck on. Just show me how to set up and work the problems and i can go from there>

1. I am a intake nurse in the emergency room with the following information:

Pay Type: HMO .17, PPO .17, Self insured .21, Uninsured .21, & All other .24
& Probability

Condition and Probability: Stroke .18, Accidnet .31, Illness .26, Other .25

a) what is the probability that the next patient through the door will be in an HMO or PPO program?

b) If having a stroke and type of insurance is independent, what is the probability that the next person through the door will be a stroke victim that is uninsured?

2. Given a population mean of 70 and variance of 169, and assuming a normal distribution:
a) What is the probablity that the next patient will have a score between 55 and 79?

b) 93% of all patients scores will be below what value?

c) 97% of all patients scores will be between what two values?

1.
(a) this would be the sum of the probabilities of an HMO or PPO (key word = "OR")

note: you don't need to subtract out the probability of HMO "and" PPO, because a person would not have both coverages - it's usually one or the other

(b) a stroke victim that is uninsured = stroke victim AND uninsured

for probabilities involving "AND", multiply them together (key word in the problem is "independent")

2.
this question uses the standard normal distribution (z scores) and the z-table found in the back of your text

take the square root of the variance to find the standard deviation, and then you've got the two pieces of info you need (mean and std dev) to solve this problem

convert the scores given in the problem to z scores z = (x - mu)/s

(a) area under the curve in between the z scores for 55 and 79
(b) find the z score corresponding to the upper 93rd percentile (divides the upper 7% and lower 93%), then convert it back to an original score
(c) same idea as (b), but you need to find the "middle" 97% of the curve
- i.e., the lower 1.5% and upper 1.5%