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A bag of 140 fair coins is dumped on a table. What is the probability that...

A bag of 140 fair coins is dumped on a table. What is the probability that the number of tails is between 65 and 80 inclusively?

Math   Statistics-And-Probability   
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Answer #1

n = 140

p = 0.5

= n * p = 140 * 0.5 = 70

= sqrt(np(1 - p))

   = sqrt(140 * 0.5 * 0.5) = 5.9161

P(65 < X < 80)

= P(64.5 < X < 80.5)

= P((64.5 - )/< (X - )/< (80.5 - )/)

= P((64.5 - 70)/5.9161 < Z < (80.5 - 70)/5.9161)

= P(-0.93 < Z < 1.77)

= P(Z < 1.77) - P(Z < -0.93)

= 0.9616 - 0.1762

= 0.7854

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