This Question: 1 pt 60t 12 (9 compete) This Quiz: 12 pls certain brand of automo

Question

This Question: 1 pt 60t 12 (9 compete) This Quiz: 12 pls certain brand of automobile tire has a mean ite span of 39,000 miles and a standard davlation of 2.050 mles (Assume the Be spans of the tires have a bell shaped distribution) (a) The Uhe spans of three randomly selected fires are 33,000 miles, 38,000 miles, and 32,000 miles Find the z-score that comespends to each e span For the e span of 33,000 miles, 7score is Round to the nearest handredth as needed) Forthe lfe span of 38.000 nlesz-score is (Round to the nearest hundredth as needed f or the lie span of 32.000 miles, -score is Round to the nearest hundredth as needed) cconding to the 2-scores would the lie spans of any of these tires be considered uns No i The te spans of tvee randomly selected Sires are 34 500 mlers 43.100mes and 39 000 miles Using the emplrical e d the pencentle that comesponds to each p

Explanation / Answer

Answer to all questions with calculations below:

Params of normal dist. are given in the question as below:

Mean - 39000
Stdev = 2050

a. X=33000, Z = X-Mu/SIGMA , Z=33000-39000/2050 =>Z=2.93
b. X=38000, Z = X-Mu/SIGMA , Z=38000-39000/2050 =>Z=-.49
c. X=32000, Z = X-Mu/SIGMA , Z=32000-39000/2050 =>Z=-3.42

Yes, anything above near 3 or -3 Z scores is Unusual.

34900 is 39000-2*2050 or 2 deviations below mean. i.e. by empirical therom it is 15.87% percentile
43100 is 39000+2*2050 or 2 deviations above mean. i.e. by empirical therom it is 84.13% percentile
39000 is 39000+0*2050 or no deviations above mean. i.e. it is 50 percentile or median

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