Probability distribution for traffic accidents

Question

Question 1: The following table contains the probability distribution for the number of traffic accidents daily in a small city:

Number of Accidents Daily (X)	P(X = xi)
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.

Question 2: If n = 5 and Π = 0.40, what is the probability that

a. X = 4?
b. X ≤ 3?
c. X < 2?
d. X > 1?

Question 3: When a customer places an order with Rudy's On-Line Office Supplies, a computerized accounting informa­tion 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 cus­tomers 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?

Question 4: Assume that the number of network errors experienced 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?

Question 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?

Question 6: Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in table above), what is the probability that

a. Z is less than 1.57?

b. Z is greater than 1.84?

c. Z is between 1.57 and 1.84?

d. Z is less than 1.57 or greater than 1.84?

Question 7: Given a normal distribution with μ = 100 and σ = 10, what is the probability that

a. X > 75?

b. X < 70?

c. X < 80 or X > 110?

d. Between what two X values (symmetrically distributed around the mean) are 80% of the values?

Question 8: In 2008, the per capita consumption of coffee in the United States was reported to be 4.2 kg, or 9.24 pounds (data extracted from en.wikipedia.org/wiki/List_of countries_ by_coffee_consumption_per_capita). Assume that the per capita consumption of coffee in the United States is approxi­mately distributed as a normal random variable, with a mean of 9.24 pounds and a standard deviation of 3 pounds.

a. What is the probability that someone in the United States consumed more than 10 pounds of coffee in 2008?

b. What is the probability that someone in the United States consumed between 3 and 5 pounds of coffee in 2008?

c. What is the probability that someone in the United States consumed less than 5 pounds of coffee in 2008?

d. 99% of the people in the United States consumed less than how many pounds of coffee?

Question 9: Consumers spend an average of $21 per week in cash without being aware of where it goes (data extracted from "Snapshots: A Hole in Our Pockets," USA Today, January 18, 2010, p. 1A). Assume that the amount of cash spent without being aware of where it goes is normally distributed and that the standard deviation is $5.

a. What is the probability that a randomly selected person will spend more than $25?

b. What is the probability that a randomly selected person will spend between $10 and $20?

c. Between what two values will the middle 95% of the amounts of cash spent fall?

Question 10: A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these calls is normally distributed, with μ = 240 seconds and σ = 40 seconds.

a. What is the probability that a call lasted less than 180 seconds?

b. What is the probability that a call lasted between 180 and 300 seconds?

c. What is the probability that a call lasted between 110 and 180 seconds?

d. 1% of all calls will last less than how many seconds?