Pulmonary Disease The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the probability of their offspring having asthma is .15; (2) if the mother is a current smoker and the father is not, then the probability of their offspring having asthma is .13; (3) if the father is a current smoker and the mother is not, then the probability of their offspring having asthma is .05; and (4) if neither parent is a current smoker, then the probability of their offspring having asthma is .04. Consider the subgroup of families in which the mother is not a current smoker. What is the probability that the father is a current smoker among such families? How does this probability differ from that calculated in Problem 3.53? * 3.53 Suppose the smoking habits of the parents are independent and the probability that the mother is a current smoker is .4, whereas the probability that the father is a current smoker is .5. What is the probability that both the father and mother are current smokers?
Pulmonary Disease The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the probability of their offspring having asthma is .15; (2) if the mother is a current smoker and the father is not, then the probability of their offspring having asthma is .13; (3) if the father is a current smoker and the mother is not, then the probability of their offspring having asthma is .05; and (4) if neither parent is a current smoker, then the probability of their offspring having asthma is .04. Consider the subgroup of families in which the mother is not a current smoker. What is the probability that the father is a current smoker among such families? How does this probability differ from that calculated in Problem 3.53? * 3.53 Suppose the smoking habits of the parents are independent and the probability that the mother is a current smoker is .4, whereas the probability that the father is a current smoker is .5. What is the probability that both the father and mother are current smokers?
Solution Summary: The author explains how the probability differs from that calculated in Problem 3.53. The probability that the father is a current smoker among such families is 0.50.
The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the probability of their offspring having asthma is .15; (2) if the mother is a current smoker and the father is not, then the probability of their offspring having asthma is .13; (3) if the father is a current smoker and the mother is not, then the probability of their offspring having asthma is .05; and (4) if neither parent is a current smoker, then the probability of their offspring having asthma is .04.
Consider the subgroup of families in which the mother is not a current smoker. What is the probability that the father is a current smoker among such families? How does this probability differ from that calculated in Problem 3.53?
*3.53 Suppose the smoking habits of the parents are independent and the probability that the mother is a current smoker is .4, whereas the probability that the father is a current smoker is .5. What is the probability that both the father and mother are current smokers?
An electronics company manufactures batches of n circuit boards. Before a batch is approved for shipment,
m boards are randomly selected from the batch and tested. The batch is rejected if more than d boards in
the sample are found to be faulty.
a) A batch actually contains six faulty circuit boards. Find the probability that the batch is rejected when
n = 20, m = 5, and d = 1.
b) A batch actually contains nine faulty circuit boards. Find the probability that the batch is rejected when
n = 30, m = 10, and d = 1.
Twenty-eight applicants interested in working for the Food Stamp program took an examination designed
to measure their aptitude for social work. A stem-and-leaf plot of the 28 scores appears below, where the
first column is the count per branch, the second column is the stem value, and the remaining digits are the
leaves.
a) List all the values.
Count
1
Stems
Leaves
4
6
1
4
6
567
9
3688
026799
9
8
145667788
7
9
1234788
b) Calculate the first quartile (Q1) and the third Quartile (Q3).
c) Calculate the interquartile range.
d) Construct a boxplot for this data.
Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
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