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Previous 12 3 4 5 6 7 8 9 10 Next Question 6 of 12 (1 point) View problem in a pop-up At a large publishing company, the mean age of proofreaders is 36.2 years and the standard deviation is 3.7 years. Assume the variable is normally distributed. Round intermediate-value calculations to two decimal places and the final answers to four decimal places. Part 1 If a proofreader from the company is randomly selected, find the probability that his or her age will be between 37.5 and 39 years. P (37.5 X 39) = 10 .13 80 Part 2 out of 2 If a random sample of 20 proofreaders is selected, find the probability that the mean age of the proofreaders in the sample will be between 37.5 and 39 years. Assume that the sample is taken from a large population and the correction factor can be ignored. Submit Assignmen Time Remaining 9 Min.

Explanation / Answer

Mean age of proof readers = 36.2 years

Standard deviation of proof readers = 3.7 years

(a) If X is the age of a random proof reader. then

Pr(37.5 < X < 39)= 0.1380 (as u calculated)

(b) Now , we took a sample of size 20.

So now standard error of sample mean se0 = s/ sqrt(n) = 3.7/ sqrt(20) = 0.827

Pr(37.5 < x < 39) = (Z2 ) - (Z1 )

where is normal standard cumulative distibution

Z2 = (39 - 36.2)/ 0.827 = 3.39

Z1  = (37.5 - 36.2)/ 0.827 = 1.572

Pr(37.5 < x < 39) = (Z2 ) - (Z1 ) = (3.39) - (1.572)

from Z table

(3.39) - (1.572) = 0.9997 - 0.9420 = 0.0577

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