18. A leading magazine (like Barron's) reported at one time that
the average number of weeks an individual is unemployed is 17
weeks. Assume that for the population of all unemployed individuals
the population mean length of unemployment is 17 weeks and that the
population standard deviation is 8 weeks. Suppose you would like to
select a random sample of 31 unemployed individuals for a follow-up
study.
Find the probability that a single randomly selected value is less
than 16.
P(X < 16) =
Find the probability that a sample of size n=31n=31 is randomly
selected with a mean less than 16.
P(M < 16) =
a) P(X < A) = P(Z < (A - )/
)
= 17
weeks
= 8
weeks
P(X < 16) = P(Z < (16 - 17)/8)
= P(Z < -0.125)
= 0.4503
b) P(M < A) = P(A -
)
)
n = 31
=
= 17
weeks
=
=
= 1.437
P(M < 16) = P(Z < (16 - 17)/1.437)
= P(Z < -0.70)
= 0.2420
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