Question

STATISTICS QUIZ 6 NAME 1. The average life of a brand of automobile tire is 30,000 miles, with a standard deviation of 2,800 miles. Ir a tire is randomly selected and tested, find the probability that it will last for more than 34,000 miles. Assume the lifetime of tires is normally distributed 2. If the tires in problem #1 are to be guaranteed, so that only 4% will have to be replaced for having to short a lifetime, how long should the warrantee be for. 3. of 760 houses burglarized in an affluent New York community, only 82 had alarm systems. Obtain a 95% confidence interval to estimate the percentage of all houses in this community with alarm systems.

Answer 1

Solution Given mmam: 301000 S.D > 2600 P(x >39000) - P(X-4 > 34000 - 30000) २800 - P(2 > 4000 ८ २९००) - P(2> |42857) - | - P(241-4257) = 1 - 0-9236 - 0-0764 ® P(xix} = 6-०५ P/-4Y-300001 २ ) - 0.04 -30000 2800 (o.0५) 1-30006 - -1.75| 28 x= -125/28 +301000 - २११50.972-

3) n = 760 x=82 = 82 760 = 0.10789 954. C.I = $ + zal * Pli-P) 0-10789 *0.892105 = 0.10789 E 1.96 * 760 = 0.10789 +0.02205 (0.08583, 0:12994) . The 95.7. confidence internal to estimate the percentage of all houses in this community with abim system is (0085€3,012994)