Question

Consider the probability that fewer than 19 out of 156 people have been in a car accident. Assume the probability that a given person has been in a car accident is 8%. Aprroximate the probability using the normal distribution. Round your answer to four decimal places. Need answer ASAP thanks!

Answer 1

Probability that a given person has been in a car accident = 0.08

n = 156

We have to find probability that fewer than 19 out of 156 people have been in a car accident

(Round to 2 decimal)

So here we have to find P( < 0.12)

n*p = 156*0.08 = 12.48>10

n*(1-p) = 156*(1-0.08) = 156 * 0.92 = 143.52 > 10

Conditions are satisfied.

According to central limit theorem if above conditions are satisfied then the sampling distribution of sample proportion is aproximately normally distributed with mean and standard deviation as follows:

Mean:

Standard deviation:

(Round to 4 decimal)

where z is standard normal variable

  

= P(z < 1.84) (Round to 2 decimal)

= 0.9671 (From statistical table of z values)

Probability that fewer than 19 out of 156 people have been in a car accident is 0.9671