Question

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 1

Answer:

a

    $P(M \ n \ J ) = 0.0802$

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 $P(J) = 0.274$

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

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

    $P(M \ n \ J ) = P(M|J) * P(J)$

    $P(M \ n \ J ) = 0.293 * 0.274$

     $P(M \ n \ J ) = 0.0802$

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]