Introductory Biostatistics

3.17 Suppose it is known that the probability of recovery for a certain disease
is 0.4. If 35 people are stricken with the disease, what is the probability
that:
(a) 25 or more will recover?
(b)Fewer than five will recover?
(Use the normal approximation.)

3.18 A study found that for 60% of the couples who have been married 10
years or less, both spouses work. A sample of 30 couples who have been
married 10 years or less are selected from marital records available at a
local courthouse. We are interested in the number of couples in this
sample in which both spouses work. What is the probability that this
number is:
(a) 20 or more?
(b)25 or more?
(c) 10 or fewer?
(Use the normal approximation.)

3.19 Many samples of water, all the same size, are taken from a river sus-
pected of having been polluted by irresponsible operators at a sewage
treatment plant. The number of coliform organisms in each sample was
counted; the average number of organisms per sample was 15. Assuming
the number of organisms to be Poisson distributed, find the probability
that:
(a) The next sample will contain at least 20 organisms.
(b)The next sample will contain no more than five organisms.

3.20 For the year 1981 (see Example 3.9), we also have the following data for
the South Atlantic states (Delaware, Florida, Georgia, Maryland, North
and South Carolina, Virginia, and West Virginia, and the District of
Columbia):

d¼7643 infant deaths

N¼ 550 ;300 live births

Find the infant mortality rate, and compare it to the national average

using the method of Example 3.9.

3.21 For atcurve with 20 df, find the areas:

(a) To the left of 2.086 and of 2.845.

(b)To the right of 1.725 and of 2.528.

(c) BeyondG2.086 and beyondG2.845.

3.22 For a chi-square distribution with 2 df, find the areas:

EXERCISES 145