Question

The Georgetown, South Carolina, Traffic Division reported 40% of high-speed chases involving automobiles result in a minor or major accident. During a month in which 50 high-speed chases occur, what is the probability that 25 or more will result in a minor or major accident? (Use the normal approximation to the binomial distribution. Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Answer 1

In Binomial distribution we compute Mean and Standard deviation as follows

Mean= n×p = 50×0.4= 20

SD=n×p×(1-p)= 50 ×0.4×0.6 =12

Thus using normal approximation when X>25 is our hypothesis or required probability.

Thus, Prob (X>25)= Prob(Z>(25-20/12)= Prob(Z>41)= 0.338

Hence, 33.8 % probability is major or minor accident .