Question

A random sample of 1000 eligible voters is drawn. Let X = the number who actually voted in the last election. It is known that 60% of all eligible voters did vote. a) Find the approximate probability that 620 people in the sample voted, and b) Find the approximate probability that more than 620 people in the sample voted.

Answer 1

n = 1000

p = 0.60

= np = 1000 * 0.60 = 600

= sqrt(np(1 - p))

= sqrt(1000 * 0.6 * 0.4) = 15.4919

a) P(X = 620)

= (619.5 < X < 620.5)

= P((619.5 - )/< (X - )/< (620.5 - )/)

= P((619.5 - 600)/15.4919 < Z < (620.5 - 600)/15.4919)

= P(1.26 < Z < 1.32)

= P(Z < 1.32) - P(Z < 1.26)

= 0.9066 - 0.8962

= 0.0104

b) P(X > 620)

= P(X > 621)

= P((X - )/> (620.5 - )/)

= P(Z > (620.5 - 600)/15.4919)

= P(Z > 1.32)

= 1 - P(Z < 1.32)

= 1 - 0.9066

= 0.0934