1. The follow table contains the probability distribution for the number of traffic accidents daily in a small city.
|
Number of Accidents Daily (X)
|
P(X = x1)
|
|
0
|
0.10
|
|
1
|
0.20
|
|
2
|
0.45
|
|
3
|
0.15
|
|
4
|
0.05
|
|
5
|
0.05
|
a. Compute the mean number of accidents per day.
b. Compute the standard deviation.
2. If n = 5 and 77- = 0.40, what is the probability that
a. X = 4?
b. X 3?
c. X < 2?
d. X > 1?
3. When a customer places an order with Rudy's On-Line Office Supplies, a computerized accounting informa-tion system (AIS) automatically checks to see if the customer has exceeded his or her credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.05. Suppose that, on a given day, 20 cus-tomers place orders. Assume that the number of customers that the AIS detects as having exceeded their credit limit is distributed as a binomial random variable.
a. What are the mean and standard deviation of the number of customers exceeding their credit limits?
b. What is the probability that zero customers will exceed their limits?
c. What is the probability that one customer will exceed his or her limit?
d. What is the probability that two or more customers will exceed their limits?
4. Assume that the number of network errors experi-enced in a day on a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 2.4. What is the probability that in any given day
a. zero network errors will occur?
b. exactly one network error will occur?
c. two or more network errors will occur?
d. fewer than three network errors will occur?
5. The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.0. What is the probability that in any particular cookie being inspected
a. fewer than five chip parts will be found?
b. exactly five chip parts will be found?
c. five or more chip parts will be found?
d. either four or five chip parts will be found?