Exam 5: Discrete Probability Distributions

The following table shows part of the probability distribution for the number of boats sold daily at Boats Unlimited. It is known that the average number of boats sold daily is 1.57. Compute the variance and the standard deviation for this probability distribution.

A continuous random variable may assume

Exhibit 5-8 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. -Refer to Exhibit 5-8. The random variable x satisfies which of the following Discrete Probability Distributions?

A company sells its products to wholesalers in batches of 1,000 units only. The daily demand for its product and the respective probabilities are given below. a.Determine the expected daily demand. b.Assume that the company sells its product at $3.75 per unit. What is the expected daily revenue?

The expected value of a random variable is

On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour. a.What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution. b.Compute the probability that exactly 5 cars will arrive in the next hour. c.Compute the probability that no more than 5 cars will arrive in the next hour.

Exhibit 5-10 The probability distribution for the number of goals the Lions soccer team makes per game is given below. -Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score no goals?

Which of the following is a characteristic of a binomial experiment?

Exhibit 5-12 The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. -Refer to Exhibit 5-12. What is the probability that in a given day there will be at least 1 accident?

Compute the hypergeometric probabilities for the following values of n and x. Assume N = 8 and r = 5. a.n = 5, x = 2 b.n = 6, x = 4 c.n = 3, x = 0 d.n = 3, x = 3

Exhibit 5-11 A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below: -Refer to Exhibit 5-11. The expected number of machine breakdowns per month is

The weight of an object is an example of

The probability distribution for the rate of return on an investment is a.What is the probability that the rate of return will be at least 10%? b.What is the expected rate of return? c.What is the variance of the rate of return?

Exhibit 5-1 The following represents the probability distribution for the daily demand of computers at a local store. -Refer to Exhibit 5-1. The probability of having a demand for at least two computers is

Exhibit 5-10 The probability distribution for the number of goals the Lions soccer team makes per game is given below. -Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score less than 3 goals?

A random variable that may take on any value in an interval or collection of intervals is known as a

The following table shows part of the probability distribution for a random variable x. a.The mean of the above distribution is known to be 1.8 . b.Compute the variance and the standard deviation for the above probability distribution.

Seven students have applied for merit scholarships. This year 3 merit scholarships were awarded. If a random sample of 3 applications (from the population of 7) is selected, a.what is the probability that 2 students were recipients of scholarships? b.what is the probability that no students were the recipients of scholarship?

In a large university, 75% of students live in dormitories. A random sample of 5 students is selected. Use the binomial probability tables to answer the following questions. a.What is the probability that the sample contains exactly three students who live in the dormitories? b.What is the probability that the sample contains no students who lives in the dormitories? c.What is the probability that the sample contains more than three students who do not live in the dormitories? d.What is the expected number of students (in the sample) who do not live in the dormitories?

A life insurance company has determined that each week an average of seven claims is filed in its Nashville branch. a.What is the probability that during the next week exactly seven claims will be filed? b.What is the probability that during the next week no claims will be filed? c.What is the probability that during the next week fewer than four claims will be filed? d.What is the probability that during the next week at least seventeen claims will be filed?