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In: Statistics and Probability

{Exercise 4.19 (Algorithmic)} The National Sporting Goods Association conducted a survey of persons 7 years of...

{Exercise 4.19 (Algorithmic)} The National Sporting Goods Association conducted a survey of persons 7 years of age or older about participation in sports activities (Statistical Abstract of the United States: 2002). The total population in this age group was reported at 248.5 million, with 120.9 million male and 127.6 million female. The number of participants for the top five sports activities appears here. Participants (millions)             Activity                                     Male                                     Female             Bicycle riding                                     20.7                                     22.5             Camping                                     24.1                                     25.8             Exercise walking                                     30.2                                     59.2             Exercising with equipment                                           18.9                                     25.9             Swimming                                     24.9                                     32.9                                     For a randomly selected female, estimate the probability of participation in each of the sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of participation in more than one sports activity. Bicycle riding Camping Exercise walking Exercising with equipment Swimming For a randomly selected male, estimate the probability of participation in each of the sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of participation in more than one sports activity. Bicycle riding Camping Exercise walking Exercising with equipment Swimming For a randomly selected person, what is the probability the person participates in exercise walking (to 2 decimals)? Suppose you just happen to see an exercise walker going by. What is the probability the walker is a woman (to 2 decimals)? What is the probability the walker is a man (to 2 decimals)?

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Given that the National Sporting Goods Association conducted a survey of persons 7 years of age or older about participation in sports activities (Statistical Abstract of the United States: 2002). The total population in this age group was reported at 248.5 million, with 120.9 million male and 127.6 million female. The number of participants for the top five sports activities appears here.

Activity Male Female
Bicycle riding 20.7 22.5
Camping 24.1 25.8
Exercise walking 30.2 59.2
Exercising with equipment 18.9 25.9
Swimming 24.9 32.9

1. For a randomly selected female, estimate the probability of participation in each of the sports activities :

Female:
Bicycle riding :22.5 / 127.6 = 0.17
Camping :25.8 / 127.6 = 0.20
Exercise walking: 59.2 / 127.6 = 0.46
Exercising with equipment: 25.9 / 127.6 = 0.20
Swimming :32.9 / 127.6 = 0.25

2. For a randomly selected male, estimate the probability of participation in each of the sports activities:

Male:
Bicycle riding :20.7 / 120.9 = 0.17
Camping :24.1 / 120.9 = 0.19
Exercise walking: 30.2 / 120.9 = 0.24
Exercising with equipment: 18.9 / 120.9 = 0.15
Swimming :24.9 / 120.9 = 0.20

3. For a randomly selected person, probability that the person participates in exercise walking =

= (59.2+30.2)/248.5

= 0.35

4. Probability the walker is a woman given that its exercise walker = P(Women and exercise walker) / P(Exercise walker)

= (59.2/248.5) / ((30.2+59.2)/248.5)

= 0.2382/0.3598 = 0.66

5.Probability the walker is a man given that its exercise walker = P(man and exercise walker) / P(Exercise walker)

= (30.2/248.5) / ((30.2+59.2)/248.5)

= 0.1216/0.3598 = 0.33.

orchestra answered 2 years ago
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