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Answer:
A) The sampling distribution for a sample size n=50 has a mean of 18.5 weeks and a standard deviation of 0.849.
B) P = 0.7616
C) P = 0.4441
Step-by-step explanation:
We assume that for the population of all unemployed individuals the population mean length of unemployment is 18.5 weeks and that the population standard deviation is 6 weeks.
A) We take a sample of size n=50.
The mean of the sampling distribution is equal to the population mean:
The standard deviation of the sampling distribution is:
B) We have to calculate the probability that the sampling distribution gives a value between one week from the mean. That is between 17.5 and 19.5 weeks.
We can calculate this with the z-scores:
The probability it then:
C) For half a week (between 18 and 19 weeks), we recalculate the z-scores and the probabilities: