The National Sporting Goods Association conducted a survey of persons 7 years of

Question

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 23.7 19.5

Camping 27.1 22.8

Exercise walking 27.2 59.2

Exercising with equipment 21.9 22.9

Swimming 27.9 35.9

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)?

Explanation / Answer

TOTAL POPULATION IS 248.5 MILLION

male population is 120.9 million

female population is 127.6 million

we have

for females we have

1. probability of a randomly selected female taking part in bicycle riding is

        =females participating in bicycle riding/total number of females=19.5/127.6=0.15 [answer]

2. probability of a randomly selected female taking part in camping is
        =females participating in camping/total number of females=22.8/127.6=0.18 [answer]

3.probability of a randomly selected female taking part in exercise walking is
        =females participating in exercise walking/total number of females=59.2/127.6=0.46 [answer]

4.probability of a randomly selected female taking part in exercise with equipment is
        =females participating in exercise with equipment/total number of females=22.9/127.6=0.18 [answer]

5. probability of a randomly selected female taking part in swimming is
        =females participating in swimming/total number of females=35.9/127.6=0.28 [answer]

for males we have

1. probability of a randomly selected male taking part in bicycle riding is

        =males participating in bicycle riding/total number of males=23.7/120.9=0.20 [answer]

2. probability of a randomly selected male taking part in camping is
        =males participating in camping/total number of males=27.1/120.9=0.22 [answer]

3.probability of a randomly selected male taking part in exercise walking is
        =males participating in exercise walking/total number of males=27.2/120.9=0.22 [answer]

4.probability of a randomly selected male taking part in exercise with equipment is
        =males participating in exercise with equipment/total number of males=21.9/120.9=0.18 [answer]

5. probability of a randomly selected male taking part in swimming is
        =males participating in swimming/total number of males=27.9/120.9=0.23 [answer]

For a randomly selected person, the probability that the person participates in exercise walking is

=total persons participating in exercise walking/total population

=(total males participating in exercise walking+total females participating in exercise walking)/total population

=(27.2+59.2)/248.5=0.35 [answer]

let A be the event that an exercise walker is going by , B be the event that the person is female, C be the event that the person is male.

Suppose you just happen to see an exercise walker going by then the probability that the walker is female is

P[B|A]=P[B and A]/P[A]=P[the person is a female excersie walker]/0.35=0.46/0.35 [answer]

Suppose you just happen to see an exercise walker going by then the probability that the walker is male is

P[C|A]=P[the person is a male excersie walker]/0.35=0.22/0.35=0.63 [answer]

activity male( million) female (million) bicycle riding 23.7 19.5 camping 27.1 22.8 exercise walking 27.2 59.2 exercising with equipment 21.9 22.9 swimming 27.9 35.9

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