In: Statistics and Probability
In 2003, it was reported that 40% of all car accidents in Connecticut were alcohol related. Suppose we take a random sample of 100 car accidents in Connecticut and let X be the number that are alcohol related.
Find the probability that at least 40 were alcohol related and at least 40 were not alcohol related.
np=100*0.40=40>10
n(1-p)=100(1-0.40)=60>10
We can use here normal approximation to binomial.
the probability that at least 40 were alcohol related
................by using continuity correction.
=P[Z>-0.10]
=1-0.4602...............................by using normal probability table.
=0.5398
Therefore,the probability that at least 40 were alcohol related is 0.5398
b) the probability that at least 40 were not alcohol related
p=1-0.40=0.60
=P[Z>-4.18]
=0.99999
the probability that at least 40 were not alcohol related is approximately 1