Exam 3: Probability Distributions

After a severe winter,potholes develop in a state highway at the rate of 5.2 per mile.Thirty-five miles of this highway pass through Washington County. a.How many potholes would you expect to see in the county? b.What is the probability of finding 8 potholes in 1 mile of highway?

A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained.Following is a record of the number of students in a class of 20 who took the test each number of times. Students Number of Tests 10 1 7 2 2 3 1 4 a.Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition. b.Find the expected value of the number of tests taken. c.Compute the variance. d.Compute the standard deviation.

In order to measure the dispersion of a random variable,look at its

The high school GPAs of applicants for admission to a college program are recorded and relative frequencies are calculated for the categories. GPA f(x) x<2.0 .08 2.0\leqx<2.5 .12 2.5\leqx<3.0 .35 3.0\leqx<3.5 .30 3.5\leqx a.Complete the table to make this a valid probability distribution. b.What is the probability an applicant's GPA will be below 3.0? c.What is the probability an applicant's GPA will be 2.5 or above?

Explain how the Poisson and exponential probability distributions relate to each other and how they relate to waiting line models.

For an exponentially distributed random variable x with a mean of 8,the probability of x  8 is .5.

The binomial probability distribution is most symmetric when p equals .5.

If x is normally distributed with mean 12 and standard deviation 2,then P(x  9)is

Experimental outcomes must occur as numerical values in order to define their probability distribution.

The weight of a .5 cubic yard bag of landscape mulch in uniformly distributed over the interval from 38.5 to 41.5 pounds. a.Give a mathematical expression for the probability density function. b.What is the probability that a bag will weigh more than 40 pounds? c.What is the probability that a bag will weigh less than 39 pounds? d.What is the probability that a bag will weigh between 39 and 40 pounds?

The Poisson probability of three events in one hour is the same as the probability of 36 events in one day.

Suppose that the arrival time for the next bus at a bus stop is uniformly distributed between 1 and 25 minutes.The probability that the bus will arrive within the next 5 minutes is 1/6.

A manufacturer of computer disks has a historical defective rate of .001.What is the probability that in a batch of 1000 disks,2 would be defective?

A probability distribution showing the probability of x successes in n trials,where the probability of success does not change from trial to trial,is termed a

The expected value of the discrete random variable x is ,a weighted average of all possible values of x.

A process follows the binomial distribution with n = 8 and p = .3.Find a.P(x = 3) b.P(x > 6) c.P(x  2)

If the Poisson distribution describes the number of occurrences per interval,the exponential distribution describes the length of the interval between occurrences.

For a binomial distribution,compare P(x = 3)when n = 10 and p = .4 to P(x = 7)when n = 10 and p = .6.

During lunch time,customers arrive at Bob's Drugs according to a Poisson distribution with  = 4 per minute. a.During a one-minute interval, determine the following probabilities: (1) no arrivals; (2) one arrival; (3) two arrivals; and, (4) three or more arrivals. b.What is the probability of two arrivals in a two-minute period? c.What is the probability that no more than 30 seconds elapses between arrivals?

Water's Edge is a clothing retailer that promotes its products via catalog and accepts customer orders by all of the conventional ways including the Internet.The company has gained a competitive advantage by collecting data about its operations and the customer each time an order is processed. Among the data collected with each order are: number of items ordered,total shipping weight of the order,whether or not all items ordered were available in inventory,time taken to process the order,customer's number of prior orders in the last 12 months,and method of payment. For each of the six aforementioned variables,identify which of the variables are discrete and which are continuous.