Suppose there is a 27.4% probability that a randomly selected person aged 40 years or older is a jogger. In addition, there is a 29.3% probability that a randomly selected person age 40 years or older is male, given that he or she jogs.

Required:
a. What is the probability that a randomly selected person age 40 years or older is male and jogs?
b. Would it be unusual to randomly select a person aged 40 years or older who is male and jogs?

Answer:

a

    [tex]P(M  \  n \  J ) = 0.0802 [/tex]

b

  Yes

Step-by-step explanation:

From the question we are told that

    The  probability that a random  selected person of age 40  years or older  is a jogger is [tex]P(J) =  0.274[/tex]

    The  probability that a random  selected person of age 40  years or older  is a male given that he/she jogs  is  [tex]P(M |J) = 0.293[/tex]

Generally the probability that a randomly selected person age 40 years or older is male and jogs

    [tex]P(M  \  n \  J ) = P(M|J) *  P(J)[/tex]

    [tex]P(M  \  n \  J ) = 0.293 * 0.274 [/tex]

     [tex]P(M  \  n \  J ) = 0.0802 [/tex]

Generally it would  be unusual  because the probability that a randomly selected person age 40 years or older is male and jogs is  greater than 0.05[border line for statistical  significance]

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