Results of a long$-$term traffic counting program produced the following results:

i$.$ The average hourly traffic during the day is $1225$ vph with a standard deviation of $307$ vph $.$

ii$.$ The evening peak hour traffic averaged $1315$ vph and had a standard deviation of $530$ vph $.$

The highway is known to have a capacity of $1940$ vph $.$ Assume the above means are based on a

large sample and the traffic volumes are normally distributed.

a$.$ What is the probability that the hourly traffic will exceed capacity?

b$.$ What is the probability that the evening peak will exceed capacity?

c$.$ How much capacity should the road have if it is to only fail $1\%$ of the time during the

evening peak period?

d$.$ If the average hourly traffic volume was found with a small sample of $18$ observations to be

$1145$ with a standard deviation of $445,$ recalculate c$).$ above.