In 1999, the American Psychological Association conducted a survey of all psycho
ID: 3048359 • Letter: I
Question
In 1999, the American Psychological Association conducted a survey of all psychologists and found that for those with 5-9 years experience who were in a rehabilitation facility, the mean income was $59,625 with a standard deviation of $11,574. Suppose that a sample of 25 psychologists with 5-9 years experience in a rehabilitation facility is obtained. Make sure that you state and check any conditions or assumptions that need to be checked and state reasons where appropriate. A) Find the probability that the average income of the 25 psychologists exceeds $70,000. State and check any conditions that might need to be checked. B) Using (A), find the probability that the total income of the 25 psychologists exceeds $1,750,000.
Explanation / Answer
A) P(X > 70000)
= P((X - mean)/SD > (70000 - 59625)/(11574/sqrt(25)))
= P(Z > 4.48)
= 1 - P(Z < 4.48)
= 1 - 1 = 0
B) P(X > 1750000/25)
= P(X > 70000)
= P((X - mean)/(SD/sqrt(n)) > (70000 - 59625)/(11574/sqrt(25)))
= P(Z > 4.48)
= 1 - P(Z < 4.48)
= 1 - 1 = 0
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