Question

Consider the probability that exactly 95 out of 145 registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 61%. Approximate the probability using the normal distribution. Round your answer to four decimal places

Answer 1

X ~ Bin ( n , p)

Where n = 145 , p = 0.61

Mean = n p = 145 * 0.61 = 88.45

Standard deviation = sqrt [ n p ( 1 - p) ]

= sqrt [ 145 * 0.61 ( 1 - 0.61) ]

= 5.8733

Using normal approximation,

P(X < x) = P(Z < ( x - Mean) / SD)

With continuity correction,

P(X = 95) = P(94.5 < X < 95.5)

= P(X < 95.5) - P(X < 94.5)

= P(Z < ( 95.5 - 88.45) / 5.8733) - P(Z < ( 94.5 - 88.45) / 5.8733)

= P(Z < 1.20) - P(Z < 1.03)

= 0.8849 - 0.8485 (From Z table)

= 0.0364