According to a 2007 report from the Center for Studying Heal

According to a 2007 report from the Center for Studying Health System Change, 38% of uninsured Americans delayed or went without medical care, often times because of concerns about cost. Assume that this percentage has not changed. A random sample of 20 uninsured individuals will be chosen. Answer the following questions and provide the probability tables for the distributions. All values should be shown to 4 decimal places.

a. Compute the expected value, E(x)

b. Compute the variance, ?

c. Compute the standard deviation, ?

d. Use excel to calculate the probability and cumulative probability distribution tables for this binomial experiment. Format the cells to number and four decimal places.

e. What is the probability that exactly seven of the sample of 20 individuals will delay or go without medical care?

f. What is the probability that fewer than seven of the sample of 20 individuals will delay or go without medical care?

g. What is the probability that at least ten of the sample of 20 individuals will delay or go without medical care?

h. What is the probability that no more than five of the sample of 20 individuals will delay or go without medical care?

i. What is the probability that between five and ten, inclusive, of the sample of 20 individuals will delay or go without medical care?

j. What is the probability that more than twelve of the sample of 20 individuals will delay or go without medical care?

Solution

a) Expected value = 20x38% = 7.6

b) variance = 7.6(0.62%) = 4.712

c) std dev = 2.17

d) Binomial probabilities

P(X=r) = 20Cr(0.38)^r)(0.62)^20-r , r =0,1,2,3,4......20

Cum prob P(X<=r) = Sum of 20Cr(0.38)^r)(0.62)^20-r, r =0,1,2....r

e) P(X=7) = 0.1774

f) P(X<7) = 0.3118

g) P(X>=10) = 0.1897