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August 22, 2014

Homework Help: statistics

Posted by Dre on Thursday, October 21, 2010 at 11:11pm.

Suppose only 75% of all drivers in a certain state regularly wear aseat belt. A random sample of 500 drivers is selected. What is theprobability that
a). Between 360 and 400 (inclusive) of the drivers in the sampleregularly wear a seat belt?
b). Fewer than 400 of those in the sample regularly wear a seatbelt?

Part b)is what I am having a hard time with. This is what I did for part a).
using a Normal approximation:
z = (400.5-500*0.75) /
sqrt(500*0.75*0.25) = 2.63

z = (359.5-500*0.75) /
sqrt(500*0.75*0.25) = -1.60

these numbers correspond to areas of 0.9957 and 0.0548, so the probability is: 0.9957-0.0548 = 0.9409

I need help solving part b).

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