Exam 6: Discrete Probability Distributions

Fans Fans arriving on a given Saturday night for a non-conference home basketball game average 0.25 per second.Let x represent the number of fans arriving at a specified time period. -What is the probability that from 10 to 12 fans arrive between 7:15 and 7:16 P.M.?

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute. -The probability that the cashier will total exactly four trays in a minute is:

Motor Co. A Motor Company has purchased steel parts from a supplier for several years and has found that 10% of the parts must be returned because they are defective.An order of 25 parts is received. What is the probability that no more than three of these parts are defective?

Stockholders The listed occupations of stockholders of a regional electric utility company included 9 percent who were homemakers.Six of these stockholders are randomly selected. -What is the probability that no stockholders are homemakers?

Distribution The probability distribution of a discrete random variable x is shown below. x 0 1 2 3 p(x) .25 .40 .20 .15 -Find the following probabilities: a.P(X > 1) b.P(X > 2) c.P(1 $\le$ X $\le$ 2) d.P(0 <X < 1) e.P(1 $\le$ X $\le$ 3)

The number of hungry people in Ethiopia is an example of a discrete random variable.

Twenty percent of the automobiles inspected at a state inspection station required repairs to meet the inspection standard.Three drivers arrive for auto inspections.Let x be the number of automobiles requiring repairs and find the probability that all three automobiles will require repair.

Approximately 14 percent of the population of Arizona is 65 years or older.A random sample of five persons from this population is taken.The probability that less than 2 of the 5 are 65 years or older is:

The listed occupations of stockholders of a regional electric utility company included 9 percent who were homemakers.If we randomly select six stockholders,compute the mean and standard deviation of the number of stockholders who are homemakers in the sample. Mean = ____________________ SD = ____________________

A business office has purchased five new electric pencil sharpeners.The manufacturer of these pencil sharpeners states that twenty in one hundred of their sharpeners will require some maintenance or repair work during the first year's use.Find the probability that at least 3 of these sharpeners will need repair during the first year.

Chocolates A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random. -What is the probability that exactly 2 pieces have nuts?

A characteristic of a Bernoulli process is that the probability of success remains the same from one trial to the next.

Given a binomial random variable with n = 15 and $\pi$ = 0.4,find the following probabilities using the binomial table. a.P(x $\le$ 12) b.P(x $\ge$ 10) c.P(x = 8) d.P(9 $\le$ x < 12) e.P(6 < x < 10)

In the following equation,what do n,x,and $\pi$ represent? $\mathrm { P } ( \mathrm { x } ) = \frac { \mathrm { n } ! } { \mathrm { x } ! ( \mathrm { n } - \mathrm { x } ) ! } \pi ^ { \mathrm { x } } ( 1 - \pi ) ^ { \mathrm { n } \cdot \mathrm { x } }$ n = __________________________________________ x = __________________________________________ $\pi$ = __________________________________________

Students Students use the university mainframe computer log-on during their designated time periods.Assume that the number of students logging on each five-minute interval is 12.5,and these log-on attempts are Poisson distributed. -Find the probability that fewer than 9 students will log-in during the next 5-minute interval.

Let x be a Poisson random variable with $\lambda$ = 8.Use the table of Poisson probabilities to find: A)P(x ≤ 6) B)P(x = 4) C)P(x ≥ 3) D)P(9 ≤ x ≤ 14)

Daisy wheel A manufacturer of daisy wheel print heads for typewriters and printers knows that 1.5% of the print heads manufactured have a defect.If a production run is 120 print heads. -Determine the probability that exactly three print heads are defective.

Appliance store A small appliance store has 10 VCR's in stock.Four of the VCR's were damaged in shipment.The owner of the store gives his daughter and his son each a VCR for a birthday present. What distribution is appropriate to determine the probability of a given number of defects? Explain why you selected your choice.

In response to a major competitor,a local pizza company begins to pay $5 to customers whose home delivered pizza did not arrive within 30 minutes after the order was placed.Assuming that the probability of a randomly selected customer having to wait more than 30 minutes is 0.01 and that 1000 customers are served tomorrow,what is the probability that the total amount paid out tomorrow will be $100 or more?

Since any value of x in a discrete probability distribution can occur only once for a given experiment,the values of x are said to be ____________________.