I am new to Statistics and am struggling to understand. Can you help? Here are m

Question

I am new to Statistics and am struggling to understand. Can you help? Here are my questions: The accounting department at Weston Materials, Inc., anational manufacturer of unattached garages, reports that it takestwo construction workers a mean of 32 hours and a standarddeviation of 2 hours to erect the Red Barn model. Assume theassembly times follow the normal distribution.    a. Determine the z values for 29 and34 hours. What percent of the garages take between 32 hours and 34hours to erect?    b. What percent of the garages takebetween 29 hours and 34 hours to erect?    c. What percent of the garages takebetween 28.7 hours or less to erect?    d. Of the garages, 5 percent take howmany hours or more to erect? I am new to Statistics and am struggling to understand. Can you help? Here are my questions: The accounting department at Weston Materials, Inc., anational manufacturer of unattached garages, reports that it takestwo construction workers a mean of 32 hours and a standarddeviation of 2 hours to erect the Red Barn model. Assume theassembly times follow the normal distribution.    a. Determine the z values for 29 and34 hours. What percent of the garages take between 32 hours and 34hours to erect?    b. What percent of the garages takebetween 29 hours and 34 hours to erect?    c. What percent of the garages takebetween 28.7 hours or less to erect?    d. Of the garages, 5 percent take howmany hours or more to erect?

Explanation / Answer

A. a z-score is just the number ofstandard deviations a number is away from a mean. in order to calculate this, you would take the (observed - mean) / standard deviation in this case, the observed is 29 and 34. (29 - 32) / 2 = -1.5 = z-score of 29 (34 -32) / 2 = 1 = z-score of 34 For the % of garages that take between 32 and 34, youwould use the proportion of z = 1 (the score of 34) and subtractthe proportion of z = 0 (the z-score of 32) Proportion (z = 1) = .8413 Proportion (z = 0) = .5 Proportion (z = 1) - Proportion (z = 0) = .8413 - .5 = .3413or 34.13% B. You would use a standard table ofnormal distributions and locate the proportions of thez-scores. Since the table gives you the proportion of everything equalto and less than the z-score, you would use the proportion of z = 1(the score of 34) and subtract the proportion of z = -1.5 (thez-score of 29) Proportion (z = 1) = .8413 Proportion (z = -1.5) = .0668 Proportion(z = 1) - Proportion(z = -1.5) = .8413 - .0668 =.7745 or 77.45% C. find the z-score of 28.7 (28.7 - 34) / 2 = -2.65 then use the table P (z = -2.65) = .0040 or 4% D. this is the same thing, but you're going backwards.According to the table, 95% or less falls within the z-score of1.745 That also means that 5% fall within the z-score of 1.745 orhigher (which is what you're trying to find) So, you take the (mean) and add 1.745(standarddeviations) 32 + 1.745(2) = 35.49 hours

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