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Probability and Frequency Distributions

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14. Due to rising medical costs, 43 million people in the United States go without medical insurance. Sample data representative of the national insurance coverage for individuals 18 years of age and older are shown below.
Medical Insurance

a. Develop adjoint probability table for these data and use the table to answer the remaining questions.
b. What do the marginal probabilities tell you about the age of the U.S. population?
c. What is the probability that a randomly selected individual does not have medical insurance coverage?
d. If the individual is between the ages of 18 and 34, what is the probability that the individual does not have medical insurance?
e. If the individual is age 35 or over, what is the probability that the individual does not have medical insurance?
f. If the individual does not have medical insurance, what is the probability that the individual is in the 18 to 34 age group?
g. What does the probability information tell you about medical insurance coverage in the United States?

medical insurance
yes no
age 18 to 34 750 170
35 and over 950 130

15. An investment banking firm submitted a bid for a project. The firm initially felt there was a 50-50 chance of getting the bid. However, the company to which the bid was submitted requested additional information on the bid. Experience indicates that on 75% of the successful bids and 40% of the unsuccessful bids the company requested additional information.
a. What is the prior probability the bid will be successful (i.e.. prior to receiving the request for additional information)?
b. What is the conditional probability of a request for additional information given that the bid wilt ultimately be successful?
c. Compute a posterior probability that the bid will be successful given that a request for additional information has been received?

16. Data were collected on the number of operating rooms in use at Homer G. Phillips Hospital over a 20-day period. On 3 of the days only one operating room was used; on 5 days, two were used; on 8 days, three were used; and on 4 days all four rooms were used.
a. Use the relative frequency approach to construct a probability distribution for the number of operating rooms in use on any given day.
b. Draw a graph of the probability distribution.
c. Show that your probability distribution satisfies the requirements for a valid discrete probability distribution.

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14. Solution:
a. The Joint Probability table is given below

AgeMedical Insurance Yes No Total
18 to 35

35 and over



b. The marginal probabilities tell us that the age group 35 and over consists more than the age group 18 to 35 in the collected sample.

c. The total number of persons does not hold a policy is 300. The number sampled is 2000. We ...

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Parallel treatments of a frequency distribution and a probability distribution.

Parallel treatments of a frequency distribution and a probably distribution.

Frequency Distribution
Complete the table below for the following data. (Recall that x is the midpoint of the interval.)

14, 7, 1, 11, 2, 3, 11, 6, 10, 13, 11, 11, 16, 12, 9, 11, 9, 10, 7, 12, 9, 6, 4, 5, 9, 16, 12, 12, 11, 10, 14, 9, 13, 10, 15, 11, 11, 1, 12, 12, 6, 7, 8, 2, 9, 12, 10, 15, 9, 3

Interval x Tally f xf
1-3 2 IIII I 6 12

Probability Distribution
A binomial distribution has n = 10 and p = .5. Complete the following table.

x P(x) x P(x)
1 .001
2 .010
3 .044
4 .117

a. Find the mean (or expected value) for each distribution.
b. Find the standard deviation for each distribution.
c. Use the normal approximation of the binomial probability distribution to find the
interval that contains 95.44% of that distribution.

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