Question

Consider the probability that greater than 99 out 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 55%.

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

Answer 1

X ~ Binomial(n,p)

Where n = 157 , p = 0.55

Mean = np = 157 * 0.55 = 86.35

Standard deviation = Sqrt(np(1-p) )

= sqrt( 157 * 0.55 * 0.45)

= 6.2336

Using normal approximation and continuity correction,

P( X < x) = P( Z < x - Mean / standard deviation)

using continuity corretion,

P( X > x) = P( X > x + 0.5)

So,

P( X > 99) = P( X > 99.5)

= P( Z > 99.5 - 86.35 / 6.2336)

= P( Z > 2.1095)

= 0.0175