## Answers

Solution:

We are given

n = 500

p = 0.5

q = 1 - p = 1 - 0.5 = 0.5

µ = Mean = np = 500*0.5 = 250

σ = SD = Sqrt(npq) = sqrt(500*0.5*0.5) = 11.18034

We have to find P(240≤X≤270) ≈ P(239.5 < X < 270.5)

P(239.5 < X < 270.5) = P(X<270.5) - P(X<239.5)

Z = (X - µ)/σ

Z = (270.5 - 250)/ 11.18034

Z = 1.833576

P(Z<1.833576) = P(X<270.5) = 0.966642

(You can find this probability by using z-table/Ti-84/83 calculator/excel/software/etc.)

Now find P(X<239.5)

Z = (239.5 - 250)/ 11.18034

Z = -0.93915

P(Z<-0.93915) = P(X<239.5) = 0.173827

(by using z-table)

P(239.5 < X < 270.5) = P(X<270.5) - P(X<239.5)

P(239.5 < X < 270.5) = 0.966642 - 0.173827

P(239.5 < X < 270.5) = 0.792815

**The probability of obtaining 240-270 successes is approximately 0.79.**

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