Question

1. The total weight of vehicles on a parking deck is uniformly distributed on the interval [200, 300] (thousands of pounds). Find the probability that the total vehicle weight is:
   1. Less than 250 thousand pounds.
   2. Between 225 and 275 thousand pounds.
   3. Between 275 and 325 thousand pounds.
   4. At least 250 thousand pounds.
2. Vehicles arrive at a car wash at an exponential rate of 7 per hour.
   1. Find the probability that the time between arrivals is between 10 and 30 minutes
   2. Find the probability that at least 15 minutes elapses without an arrival.
   3. Find the time t where there is a 50% chance that the next customer arrives within t minutes of the last.
3. The attendance at a college athletic event can be approximated with a normal distribution that has a mean of 10,000 and a standard deviation of 2300.
   1. Find the probability that an athletic event’s attendance is less than 12,000.
   2. Find the probability that an athletic event’s attendance is less than 5000.
   3. Find the probability that an athletic event’s attendance is between 12,000 and 14,000.
   4. Find the probability that an athletic event’s attendance is at least 7700.
   5. Find the probability that an athletic event’s attendance is between 8000 and 11,000.
   6. 20% of games have an attendance below what level?
   7. 10% of games have an attendance above what level?

Answer 1

For the weigth of the vehicles:

a) Probability of weight less than 250 = 0.5

b) Probability of weight between 225 and 275 = 0.5

c) Probability of weight 275 and 325 = 0.25

d) Probability of weight of atleast 250 = 0.5