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Business Statistics_CH 5
Chapter 5 take-home exam
64
Business
03/29/2010

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Term
Random Variable
Definition
A variable that takes on different numerical values based on chance
Term
Discrete Random Variable
Definition
A random variable that can only assume a finite number of values or an infinite sequence of values such as 0,1,2,3....
Term
Continuous Random Variables
Definition
Random variables that can assume any vallue in an interval.
Term
Expected Value
Definition
The mean of a probability distribution. the average value when the experiment that generates values for the random variables is repreated over the long run.
Term
Binomial Probability Distribution characteristics
Definition
A distribution that gives the probability of x successes in n trials in a process that meets certain conditions.
Term
Binomial Prob. Dist. characteristics #1
Definition
a trial has only two possible outcomes; a success or a failure.
Term
Binomial Prob. Dist. characteristics #2
Definition
There is a fixed number, n, identical trials.
Term
Binomial Prob. Dist. characteristics #3
Definition
The trials of the experiment are independent of each other. this means that if one outcome is a success, this does not influence the chance of another outcome being a success.
Term
Binomial Prob. Dist. characteristics #4
Definition
The process must be consistent in generating successes and failures. that is, the probability. p, associated with a success remains constant from trial to trial.
Term
Binomial Prob. Dist. characteristics #5
Definition
if p represents the probability of a success, then (1-p) = q is the probability of a failure.
Term
Hypergeometric distribution
Definition
is formed by the ratio of the number of ways an event of interest can occur over the total number of ways any event can occur.
Term
The binomial Dist. is useful when...
Definition
it is useful when the value of a discrete random variable is based on independent trials and when on a given trial there are two possible outcomes and we can count the number of successes and failures.
Term
Poisson Dist.
Definition
Deals with situations in which the trials are independent but we are able to count only the sucesses.
Term
Hypergeometric dist.
Definition
applies when the trials are dependent and the sample size is large relative to the size of the finite population.
Term
False
Definition

 

True/False: if a random variable is discrete, it means that the outcome for the random variable can take on only one of two possible values.

Term
True
Definition

 

True/False: the random variable, number of customers entering a store between 9AM and noon, is an example of a discrete random variable.

Term
True 
Definition

 

True/False: When a single value is randomly chosen from a discrete distribution, the different possible values are mutually exclusive.

Term
False
Definition
True/False: The Colbert Real Estate Agency has determined the number of home showings given by its agents is the same each day of the week. then the variable-number of showings-is a continuous dist.
Term
True
Definition
True/False: The time required to assemble two components into a finished part is recorded for each employee at the plant. the resulting random variable is an example of a continuous random variable.
Term
False
Definition

True/False:The Cromwell company has the opportunity to enter into a contract to build a mountain road. the following table shows the probability for the profit that could occur if they ta0ke the contract:

profit probability

$30,000_0.15

$50,000_0.20

$70,000_0.30

$100,000_0.35

Based on this info. the expected profit for the company if they take the contract is $60,000.

Term
False
Definition
True/False: a prob. dist. with an expected value greater than the expected value of a second prob. dist. will also have a higher stand. dev.
Term
True
Definition

True/False: the number of no-shows each day for dinner reservations at the cottonwood Grille is a discrete random variable with the following prob. dist.

No-shows prob.

0_0.30

1_0.20

2_0.20

3_0.15

4_0.15

based on this info. the expected number of no-shows is 1.65 customers.

 

Term
True
Definition
True/False: the number of calls to an internet service provider during the hour between 6:00 and 7:00 pm is described by a poisoon dist. with a mean equal to 15. given this info. the expected number of calls in the first 30 min. is 7.5 calls.
Term
False
Definition

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following prob. dist.

No-show Prob

0_0.30

1_0.20

2_0.20

3_0.15

4_0.15

Based on this info. the standard deviation for the number of no-shows is about 0.36 customers.

Term
True
Definition
True/False: A construction company has found they have a prob. of 0.10 of winning each time they bid on a project. the prob. of winning a given number of projects out of 12 bids could be determined with a binomial dist.
Term
True
Definition
True/false: Bill price is a sales rep in northern California representing a line of athletic socks. each day, he makes ten sales calls. the chance of making a sale on each call is thought to be 0.30. the prob. that he will make exactly two sales is approx. 0.2335
Term
true
Definition
True/False: Each week American stores receives a shipment from a supplier. the contract specifies that the maximum allowable percent defective is 5 percent. when the shipment arrives, a sample of 20 parts is randomly selected. if 2 or more of the sampled parts are defective, the shipment is rejected and returned to the supplier. assume that a shipment arrives that actually has 4% defective parts and the dist. of defective parts is described by a binomial dist. then the prob. that the shipment is rejected is approx. 0.19.
Term
True
Definition
True/False: when using the binomial dist. the maximum poss. number of success is the number of trials.
Term
False
Definition
True/False: The Nationwide Motel company has determined that 70% of all calls for motel reservations request non-smoking rooms. recently, the service manager for the company randomly selected 25 calls. assuming that the dist. of calls requesting non-smoking rooms is described by a binomial dist, the expected number of request for non-smoking rooms is 14.
Term
False
Definition
True/False: The dist. for the number of emergency calls to a city's 911 emergency number in a one-hour time period is likely to be described by a binomial Dist.
Term
True
Definition
True/False: The Hawkins company randomly samples 10 items from every large batch before the batch is packaged and shipped. according to the contract specifications, five percent of the items can be defective. if the inspectors find 1 or fewer defects in the sample of ten, they ship the batch without further inspection. if they find 2 or more, the entire batch is inspected. based on this sampling plan, the prob. that a batch that meets that contract requirements will be shipped without further inspection is approximately .9138
Term
False
Definition
True/False: the primary difference between the binomial dist. and the poisson dist. is that the poisson is used to describe a continuous random variable and the binomial is used for discrete random variables.
Term
False
Definition
True/False: the number of customers that arrive at a fast-food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. the prob that more than 4 customers will arrive in a 30-min. period is .1933
Term
True
Definition
True/False: the number of customers that arrive at a fast-food business during a one-hour period is known to be poisson distributed with a mean equal to 8.60. the prob that betwen 2 and 3 customers inclusively will arrive in one hour is 0.0263.
Term
True
Definition
True/False: The makers of crustfree bread in boston have a quality standard that allows no more than 3 burned loaves per batch on average. recently, the manager inspected a batch and found 5 burned loaves. she did not appear to be upset at the production meeting. this is because the chances of exactly 5 burned loaves occuring is 0.1008
Term
True
Definition
True/False: The primary application for the hypergeometric prob dist. is in situations where the sampling is done without replacement from a finite population.
Term
Uniform Distribution
Definition
A store sells six different models of cell phones and have found that they sell an equal number of each model. the probability dist. that would descrive this random variable is called:
Term
Discrete probability dist.
Definition

The following prob. dist. has been assessed for the number of accidents that occur in a midwestern city each year

accidents probability

0_0.25

1_0.20

2_0.30

3_0.15

4_0.10

this dist. is an example of....

Term
0.45
Definition

The following dist. has been assessed for the number of accidents that occur in a midwestern city each year.

Accidents Probability

0_0.25

1_0.20

2_0.30

3_0.15

4_0.10

The prob. of having less than 2 accidents on a given day is:

Term
1.65
Definition

The following probability dist. has been assessed for the number of accidents that occur in a midwestern city each day:

accidents probability

0_0.25

1_0.20

2_0.30

3_0.15

4_0.10

Based on this dist., the expected number of accidents in a given day is...

Term
1.28
Definition

The following probability dist. has been assessed for the number of accidents that occur in a midwestern city each day.

accidents probability

0_0.25

1_0.20

2_0.30

3_0.15

4_0.10

Based on this prob dist., that standard deviation in the number of accidents per day is...

Term
0.15
Definition

A sales rep for a national clothing company makes 4 calls per day. based on historical records, the following prob. dist. describes the number of successful calls each day:

successful calls probability

0_0.10

1_0.30

2_0.30

3_0.20

4_0.10

Based on this info, the prob. that the sales rep will have a total of two successful calls in a two-day period is...

Term
0.60
Definition

A sales rep for a national clothing company makes 4 calls per day. based on historical records, the following prob dist. describes the number successful calls each day..

successful calls probability

0_0.10

1_0.30

2_0.30

3_0.20

4_0.10

Based on the information provided, what is the prob. having at least 2 successful calls in one day?

Term
A-Dist a has a higher variance
Definition

Consider the following two prob. dist.

Dist. A      Dist. B

0_0.20      0_0.01

1_0.20      1_0.02

2_0.20      2_0.94

3_0.20      3_0.02

4_0.20      4_0.01

Which of the following is an accurate statement regarding these two dist?

A-dist.a has a higher variance

B-dist b has a higher variance

C-both dist are positivily skewed

D-both dist. are uniform.

 

 

Term
0.0746
Definition
A package delivery service claims that no more than 5 percent of all packages arrive at the address latre. assuming that the conditions for the binomial hold, if a sample of siz 10 packages is randomly selected, and the 5 percent rate holds, what is the prob that exactly 2 packages in the sample arrive late?
Term
0.0116
Definition
The package delivery service claims that no more than 5% of all packages arrive at the address late. assuming that the conditions for the binomial hold, if a sample size of 10 packages is randomly selected and the 5% rate holds, what is the prob. that more than 2 packages will be delivered late?
Term
0.9832
Definition
The Vardon Exploration Company is getting ready to leave for South America to explore for oil. one piece of equipment requires 10 batteries that must operate for more than 2 hours. the batteries being used have a 15% chance of failing within 2 hours. the exploration leader plans to take 15 batteries. assuming that the conditions of the binomial apply, the prob. that the supply of batteries will contain enough good ones to operate the equipment is...
Term
10
Definition
Many people believe that they can tell the difference between Coke and Pepsi. other people say the two brands can't be distinguished. to test this, a random sample of 20 adults was selected to participate in a test. after being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. if people really can't tell the difference, the expected number of correct indentifications in the sample would be...
Term
A
Definition

Many people believe that they can tell the difference between Coke and Pepsi. other people say the two brands can't be distinguished. to test this, a random sample of 20 adults was selected to participate in a test. after being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. Suppose 14 peopl correctly identified the soft drink brand. which of the following conclusions would be warranted under the circumstances?

a-since the prob of getting 14 or more correct is 0.0577 which is quite low, the conclusion could be that people are effective at identifying soft drink brands.

b-since the prob of getting 14 or more correct is 0.0577 which is quite low, this means that people are not effective in identifying the soft drink brand.

c-since the chance of getting 14 correct is 0.0370 which is quite small, the study shows that people are not able o identify brands effectively

d- the expected value for this binomial dist. is very close to 14 so this supports that people cannot tell tghe difference.

Term
5
Definition
If the number of defective items selected at random from a parts inventory is considered to follow a binomial distribution with n=50 and p=0.10, the expected number of defective parts is...
Term
binomial dist.
Definition
If a study is set up in such a way that a sample of people is surveyed to determine whether they have ever used a particular product, the likely probability distribution that would describe the random variable-the number who say yes-is a:
Term
Poisson Dist.
Definition
Assuming that potholes occur randomly along roads, the number of potholes per mile of road could best be described by the:
Term
10.5
Definition
The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 3.5. Based on this, how many defects should be expected if 3 containers are inspected?
Term
0.0821
Definition
The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that no customers will arrive in a 15 minute period?
Term
0.4703
Definition

The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that 2 or 3 customers will arrive in a 15-minute period?

Term
0.0067
Definition

If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability of 0 cars arriving in a given hour?

Term
0.1755
Definition

If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability that exactly 5 cars will arrive during a given hour?

Term
0.9569
Definition

The number of weeds that remain living after a specific chemical has been applied averages 1.3 per square yard and follows a Poisson distribution. Based on this, what is the probability that a 1 square yard section will contain less than 4 weeds?

Term
0.5665
Definition

The manager of a movie theater has determined that the distribution of customers arriving at the concession stand is Poisson distributed with a standard deviation equal to 2 people per 10 minutes. What is the probability that more than 4 customers arrive during a 10 minute period?

Term
9
Definition

If the standard deviation for a Poisson distribution is known to be 3, the expected value of that Poison distribution is:

Term
10 and 11
Definition

If a distribution is considered to be Poisson with a mean equal to 11, the most frequently occurring value for the random variable will be:

Term
the sampling is performed without replacement from a finite population
Definition

The hypergeometric probability distribution is used rather than the binomial or the Poisson when:

Term
0.417
Definition

A small city has two taxi companies (A and B). Each taxi company has 5 taxis. A motel has told these companies that they will randomly select a taxi company when one of its customers needs a cab. This morning 3 cabs were needed, assuming that no one individual taxi can be used more than once, what is the probability that 2 of the cabs selected will be from Company A and the other will be from B?

Term
Approximately .08
Definition

A local paint store carries four brands of paint (W, X, Y, and Z). The store has 5 cans of W, 3 cans of X, 6 cans of Y, and 15 cans of Z, all in white. It is thought that customers have no preference for one of these brands over another. If this is the case, what is the probability that the next five customers will select one can of W, X, Y and two cans of brand Z?