SOLUTION: A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 39 weeks. Assume that for the population of all unemployed i

Question 1119450: A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 39 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 39 weeks and that the population standard deviation is 2 weeks. Suppose you would like to select a random sample of 35 unemployed individuals for a follow-up study.
Find the probability that a single randomly selected value is less than 38.
P(X < 38) =
Find the probability that a sample of size n=35 is randomly selected with a mean less than 38.
P(M < 38) =
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 39 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 39 weeks and that the population standard deviation is 2 weeks. Suppose you would like to select a random sample of 35 unemployed individuals for a follow-up study.
Find the probability that a single randomly selected value is less than 38.
P(X < 38) =
z(38) = (38-39)/2 = -.958/2
P(x < 38) = P(z < -1/2) = normalcdf(-100,-0.5) = 0.3085
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Find the probability that a sample of size n=35 is randomly selected with a mean less than 38.
P(M < 38) =
z(38) = (38-39)/(2/sqrt(35)) = -sqrt(35)/2 = -2.9580
p(M < 38) = P(z < -2.9580) = normalcdf(-100,-2.9580) = 0.0015
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Cheers,
Stan H.
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