Question

Consider the probability that more than 93out of 157 people have not been in a car accident. Assume the probability that a given person has not been in a car accident is 60%.

Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answer 1

n = 157

p = 0.6

= n * p = 157 * 0.6 = 94.2

= sqrt(np(1 - p))

    = sqrt(157 * 0.6 * 0.4)

    = 6.1384

P(X > 93) = P(X > 94)

               = P(X > 93.5)

               = P((X - )/> (93.5 - )/)

               = P(Z > (93.5 - 94.2)/6.1384)

               = P(Z > -0.11)

              = 1 - P(Z < -0.11)

              = 1 - 0.4562

              = 0.5438