Questions and Answers of Principles Of Managerial Statistics

You and your partner are the owners of a company that specializes in remodeling houses and interior design. You would like to track the time between complaints (in months) but do not know how. Your
A laptop manufacturer produces laptops with a mean life of seven years. What warranty should they offer such that no more than 25% of the laptops will fail before the warranty expires? Assume laptop
Determine if the following defines a discrete or continuous random variable:a) Time it takes to complete a product in an assembly line.b) Tire pressure after a stress and safety test.c) Number of
The travel time for a university student between her home and her favorite nightclub is uniformly distributed between 15 and 25 minutes. Find the probability that she will finish her trip in 22
From the following illustrations, determine if the probability is greater than 0.5, lower than 0.5, or cannot be sure. (a) (d) (b) (c) AAA (e) (f)
Show that for a normal distribution, the probability withina) 1.28 standard deviations from the mean is 0.80.b) 1.96 standard deviations from the mean is 0.95.c) 2.57 standard deviations from the
For a normally distributed random variable, find the probability of fallinga) More than 2.33 standard deviations above the mean.b) Within 0.33 standard deviations from the mean.
For a normally distributed random variable, find the z-score that is 0.75 standard deviations from the mean.
The weight of a model of computer laptops, X, is normally distributed with a mean of 2.8 pounds and a standard deviation of 0.1 pounds. What argument would you use to state that P(X ≤ 2.6) = P(X
Suppose you are given the option of choosing from two production procedures. Both have possibilities that follow a normal distribution. One has mean profit of $280 and standard deviation $10.Theother
There is a situation where you wish to find P(X < 3) for some continuous random variable X. You assume that the random variable X follows a normal distribution with mean 10 and standard deviation
Lightning strikes are a forest fire hazard. Therefore, it is important to model lightning strike patterns within a region. If time between lightning strikes for a region follows an exponential
State whether the given probability is theoretical, empirical, or subjective.a) A poll of registered voters found that 38% of participants plan to vote for candidate X.b) In poker, the probability of
Which of the following cases does not define a proper probability distribution. Explain.a) Case Ab) Case Bc) Case C X 0 1 P(X = X) 0.60 0.14
A wide variety of data sets such as tax returns, population sizes, and power consumption tend to comply with what is known as Benford’s law, which establishes a frequency distribution for the
A company is evaluating the potential of a future project. Y is their profit, which depends on several uncertain factors. They have determined that their profit could be $1, $1.75, and $2.35 million
If E(X) = 40, E(Y) = 25, Var(X) = 3, Var(Y) = 2, and X is independent ofY, finda) E(5).b) E(2X).c) E(3X + 5Y).d) E(7X − 3Y).e) Var(12).f) Var(7Y).g) Var(3X + 5Y).h) Var(3X − 5Y).
If E(X) = 100, E(Y) = 225, Var(X) = 10, Var(Y) = 25, and Cov(X, Y) = 10, finda) E(70X − 35Y).b) Var(70X + 35Y).c) Var(70X − 35Y).d) If Cov(X, Y) = −5, find Var(70X − 35Y).
If X1,X2, and X3 each are independent and have an expected value of 10, find X+X+X 3 ( X₁ + X ₂ + X ₂ ) ). 3 a) E b) Var
The expected revenue for a new product is $20 million. It is known that the total costs will be $15 million. What would the expected profit be?
A gas station sells two types of gasoline: regular and premium. Let X be the amount (in gallons) of regular sold in a day and Y = amount (also in gallons) of premium sold in a day. Regular is priced
Two weeks ago, you were hired as a manager for one of the top companies headquartered in Houston, Texas. Unfortunately, a storm close by in the Gulf of Mexico has quickly gained strength and has
In each case, determine if a binomial random variable is in play. If the random variable does not follow a binomial distribution, state why.a) Waiting time of 10 people to be attended at an emergency
X ∼ binomial(10, 0.75). Without making a calculation, will P(X = 2) be larger than, equal to, or smaller than P(X = 8)? Explain.
X ∼ binomial(10, 0.75). Find P(X = 2) and P(X = 8). Compare.
If X follows a binomial(25, 0.40), determinea) P(X = 1).b) P(X = 10).c) P(X ≥ 1).d) P(X > 1).e) E(X).f) Var(X).g) Standard deviation of X.
If X follows a binomial(5, 0.15), determinea) P(X = 0).b) P(X ≤ 4).c) P(X ≥ 1).d) P(X > 1).e) E(X).f) Var(X).g) Standard deviation of X.
If X follows a binomial(10, 0.60) and Y follows a binomial(10, 0.10),a) Without doing a calculation, would P(X = 4) be smaller than, greater than, or equal to P(Y = 4)? Explain.b) Find P(X = 4) and
Based on a true story! In Costa Rica, there are howling monkeys living in mango trees. People sometimes annoy them and they will throw mangoes at the people. Five tourists arrive in a car and start
A student in a statistics course forgets to study for a multiple choice exam. Since the student does not understand the material, they must randomly guess the correct answer to each question (from
Which of the following random variables are candidates to be modeled with a Poisson distribution:a) Number of car accidents at an intersection on a Tuesday night.b) Time it takes a machine to
If X follows a Poisson(5), determinea) P(X = 1).b) P(X = 10).c) P(X ≥ 1).d) P(X > 1).e) E(X).f) Var(X).g) Standard deviation of X.
You and your partner are the owners of a company that specializes in remodeling houses and interior decoration. You would like to track the amount of complaints you get a month, but do not know how.
The number of lightning strikes in a year for a region in central United States has a Poisson distribution with a mean of 4.9. Find the probability that in a randomly selected year, the number of
Find the value of the missing probability (or probabilities) such that the table defines a proper probability distribution function:a) Case 1b) Case 2c) Case 3 250 750 950 P(X = X) 0.35 0.25
State what are the five main properties of a random variable that follows a binomial distribution.
Every fall, managers at a bank run a marketing campaign to promote their credit card to customers. The marketing pitch will be presented to a random sample of 20 customers visiting the bank.
For Example 6.15, the keen reader may have wondered why use a Poisson distribution to find probabilities, instead of the empirical probabilities. The table below presents the empirical
A firm will randomly draw credit data of 500 households at once in a town of 1 000 households. If X = number of households in the random sample with credit debt of at least $5 000, does this random
A professor receives 20 exams from his 20 students. After grading 10exams, she checks the enrollment and sees 3 people dropped the class. She now has 17 students. If she grades the exams at random,a)
Show that when rolling a dice, getting an even number and getting a number greater than 3 are not mutually exclusive events.
Determine what event would not be able to occur at the same time with the following events (the events are mutually exclusive):a) You roll a die and get an even number.b) Voter supports a candidate
Suppose a dice is rolled once.a) Define A = result is greater than 2 and even. What are the possible outcomes that form this event?b) Define B = result is greater than 5 and a prime number (only
A company wishes to conduct an analysis on the strength of some rods they produce. What is the sample space of the experiment?
Yesterday, the local weatherman indicated that there was a 70% chance of rain. At the end of the day, it did not rain. Explain why the fact that it did not rain does not mean the local weatherman was
Based on the table below, evaluate each interpretation to determine if correct. Explain how the incorrect interpretations are wrong.a) The majority of plant managers consider the new machines to be
Before starting a new project, an analyst in a firm you work at determined that the probability the project would exceed its budget was 17%. Eventually, the project exceeded its budget. Was the
A professional basketball team is one of the two remaining for the championship. The data analytics staff for the team has estimated that the probability of the team winning it all is 80%.The players
A grocery store has calculated that the empirical probability of not running out of milk in any given day is 86%. Based on this probability, on average, how many times will they run out of milk in
Define the following notation for the population of students at your local university:F = the event that a student is female.M = the event that a student is male.B = the event that a student is from
If P(A) = 0.15, P(B) = 0.44, and P(A or B) = 0.29. Finda) P(Ac)b) P(Bc)c) P(A and B)
If P(A) = 0.4, P(B) = 0.35, and P(A and B) = 0.15. Finda) P(Ac)b) P(Bc)c) P(A or B)
One die is rolled. Find the probability of gettinga) A one.b) An even number.c) An even and uneven number.d) A four and an even number.e) A one or an uneven number.
If P(A) = 0.6, P(B) = 0.45, and P(A and B) = 0.25. Finda) At least one of the two events occurs.b) A occurs B occurs but not both simultaneously.
Given that P(A) = 0.25, P(B) = 0.5, and P(A and B) = 0.1. Find P((A or B)c).
Two dice are rolled. Find thea) Number of possible outcomes in the experiment.b) Probability of getting the same number in each die.c) Probability of getting a 2 in one die or a 5 in one die.
P(A) = 0.5, P(B) = 0.3. It is known that if B occurs, then A will certainly occur. Find P(A and B) and P(A or B).
Concerned about the economy, the CEO of a marketing strategy company asks analysts to determine the probability of low demand of their services next year (L), of high demand (H), and of losses of at
If P(A) = 0.4, P(B) = 0.35, and P(A and B) = 0.05. Finda) P(A|B)b) P(B|A)c) Are events A and B independent? Explain
If P(A) = 0.6, P(B) = 0.45, and P(A and B) = 0.27. Finda) P(A|B)b) P(B|A)c) Are events A and B independent? Explain
Given that P(A) = 0.10, P(B) = 0.35, and P(A and B) = 0.07.a) Are these two events independent? Explain.b) Calculate P(A|B).c) Calculate P(B|A).
P(B) = 0.35 and P(B|A) = 0.70. If B is something we hope occurs, do we want A to occur or not? Explain.
P(A) = 0.67 and P(B) = 0.52, and A and B are mutually exclusive. Find P(B|A).
The concept of conditional probabilities can be extended to more than two probabilities. If P(A|B and C and D) = P(A)a) Does it mean A is independent from event (B and C and D)? Explain.b) Does it
In multiple choice questions, there is always the possibility that a student luckily guesses the right answer. Suppose K = student knows the right answer, C = student answers correctly. If three
Define A = {1, 4, 6, 7}, B = {3, 6, 9}, C = {5, 8, 9}.a) What are the outcomes in the event A or B?b) What are the outcomes in the event A and B?c) What are the outcomes in the event A or B or C?
The table below shows the type of incidents that lead to a call to the Fire Department in Detroit in 2015.a) What is the probability the incident is a false alarm?b) What is the probability the
The following contingency table describes type of Cheese produced and whether it is organic based on 1296 companies from Canada. Find each probability.a) P(O)b) P(Y and R)c) P(O|Y)d) P(V or N)e) P(R
Figure 3.16 suggested that race was related to whether a male driver was searched by police in San Diego in 2016. When exploring this question, it is important to consider the cause of the traffic
Female drivers are searched less often than men during police stops. But is there evidence that race predicts whether a female driver was searched by police in San Diego in 2016? The Table summarizes
Find the numerical value of 3!.
Find the numerical value of 4!.
Solve the following combinatoric expressions:a) 10 choose 2.b) 5 choose 0.c) 7 choose 7.d) 5 choose 2.
Orlando building permits from 2010 to 2015 can be downloaded (File “Orlando_Building_Permits_Issued”).a) Find the probability that a building permit is of type “ROOF”?b) Construct a bar chart
Use Table 5.5 and P(D1) = 0.1263, P(D2) = 0.1433, P(D3) = 0.1452, P(D4) = 0.1467, P(D5) = 0.1467, P(D6) = 0.1518, and P(D7) = 0.1400 to show that the probability there is a missing person report in
In an effort to increase the number of listeners, radio station WHACK-95.1 FM is doing sweepstakes for $50 000. The caller has to guess a four digit number to win the prize. The administration
If a six-sided die is tossed two times and “3” shows up both times, what is the probability of “3” on the third trial? Explain.
Given that an experiment has only outcomes associated to three events, A, B,C, while P(A) = 0.5, P(B) = 0.4, P(C) = 0.1, and P(A and B and C) = 0. Can any of these events happen simultaneously?
If P(A) = 0.22, P(B) = 0.47, and P(A and B) = 0.22. Finda) P(B|A)b) P(A|B)c) If you want B to happen, is it preferable for A to happen, not happen, or it does not matter?d) If you want A to happen,
As you will see later on, one way to perform statistical inference is based on conditional probabilities. That is, a person wishing to infer on whether μ > 22 may find the probability of some
We have two independent events such that P(A) = 0.35 and P(B) = 0.25.a) What is the probability of the event: “A occurs and B does not occur”b) What is the probability of the event: “A, B do
At the beginning of 2017, managers and directors at Las Vegas were surveyed on their satisfaction with IT services.Their responses can be found in the file “IT_Satisfaction_Survey.” Use the data
A business is assessing the performance of their advertising campaign for healthy snacks. They conducted a survey of people that had not used the product before the ad campaign and the results are
On a statistics test, the third quartile for scores was 82. What is the interpretation of the third quartile in the context of this situation?
If the intention is to get a measure of monthly United Airlines landings at the San Francisco airport, the data used in Problem 3.11 is too detailed. Specifically, at least one category of the
University administrators record data from their students. For example, using admission records, they determine that 1075 was the mean SAT score of the latest business program freshmen. Is the number
Search online to see if cities near to your school have an open data portal. Download in CSV form data you consider interesting.
Data on daily units and legal sales (in $) of several marijuana products in Washington since July 2014 are available online. A Minitab snapshot of the data is presented below.a) What variable does
Below you will find 2015 data for several community statistical areas within Baltimore, as seen with Excel. The top row is the variable name, and the second row defines each variable. The rest of the
2012 mean total SAT scores per New York City school are available to the public. The original data set provides location, number of test takers, and scores on Critical Reading, Math, and Writing.a)
It is not always straightforward to open data files using statistical software.a) Open “Chicago_Public_Schools_-_School_Profile_Information_ SY1617.csv” using Excel.b) Open
Determine if the following are structured or unstructured data.a) Driver’s reaction time while using a cell phone.b) Brand of tablet.c) Blog content.
Determine if the following are structured or unstructured data.a) Video feedb) Tweets by a celebrityc) Vehicle average speed
Classify each variable as numerical or categorical.a) Number of hours of study a week.b) Favorite class this semester.c) Weight of your cell phone.d) Miles per gallon of a car.e) Car model.
Determine the level of measurement (nominal, ordinal) in the following problems.a) How much a person likes a pair of shoes (from not at all to a lot).b) Gaming app installed on phone (Yes, No) by
In the following, state if the numerical variable is discrete or continuous according to their possible values.a) X = 0, 1, 2, 3b) Y = 10, 15, 42c) 5 < Y < 73d) Z ≥ 152
In the following, state if the numerical variable is discrete or continuous.a) Number of times there was a power outage somewhere in the United States last year.b) Volume of chocolate by 25 kids
As in Problem 2.11, state if the numerical variable is discrete or continuous.a) Distance traveled by an automobile until it makes a full stop.b) Number of faulty products that come from an assembly
Placing at amarathon, do you think it counts as a categorical or numerical value?
A player’s sport team number, is that considered a numerical or categorical variable?

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