Question

A fair coin is flipped 30 times. If X = the number of H s, then the approximate value of P(X = 15) is..

a) .074

b) .193

c) .097

d) .146

Answer 1

For this example, we have

n = 30

p = 0.5

q = 1 - p = 0.5

Mean = np = 30*0.5 = 15

SD = sqrt(npq) = sqrt(30*0.5*0.5) = 2.738612788

We have to find P(X=15) = P(14.5<X<15.5)

P(14.5<X<15.5) = P(X<15.5) - P(X<14.5)

Find P(X<15.5)

Z = (X - mean)/SD = (15.5 - 15)/ 2.738612788 = 0.182574186

P(Z<0.182574186) = 0.57243393

(by using z-table)

Now find P(X<14.5)

Z = (X - mean)/SD = (14.5 - 15)/ 2.738612788 = -0.182574186

P(Z<-0.182574186) = 0.42756607

(by using z-table)

P(14.5<X<15.5) = 0.57243393 - 0.42756607 = 0.146

Answer: d) .146