Question

In: Statistics and Probability

Consider the probability that greater than 99 out of 157 people have not been in a...

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.

Solutions

Expert Solution

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


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