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business
principles of managerial statistics

Questions and Answers of Principles Of Managerial Statistics

The 2015 average commute time (in minutes) in a West Hills, Los Angeles, census tract was 29.9. Let X = commute time to work and Z = the usual standardized random variable. Assuming a normal
Determine if the probability notation is adequate in each case when Z ∼ N(0, 1). Fora) X ∼ N(32.5, 6.3), the probability that the random variable is less than 37.48 is P(Z < 37.48).b) X ∼
Calculate each probability.a) P(X ≤ 612) when X ∼ N(725,100).b) P(X > 11.44) when X ∼ N(15.05, 3.45).c) P(252 < X ≤ 277) when X ∼ N(245, 25).
Calculate each probability.a) P(X > 113) when X ∼ N(50, 3).b) P(59 ≤ X ≤ 81) when X ∼ N(65, 2).c) P(X ≤ 7) when X ∼ N(30, 2).
For each scenario, determine the value of X.a) The 10th percentile when X ∼ N(275, 10).b) The 90th percentile when X ∼ N(25, 2).
For each scenario, determine the value of X.a) Such that 70% of values of X are greater and X ∼ N(30, 5).b) Such that there is a 66%chance that P(−x ≤ X < x) when X ∼ N(55, 3).
A company owns two stores. The monthly profit of the first store follows a normal distribution with mean $10000 and standard deviation $1000. The monthly profit of the second store follows a normal
A company owns two stores. The monthly profit of the first store follows a normal distribution with mean $10000 and standard deviation $1000. The monthly profit of the second store follows a normal
The 2016 combined (math and critical reading) mean SAT scores for college-bound females was 987 and the standard deviation was 162.64. The scores were normally distributed. If a college program
If X ∼ N(80, 10), show thata) The 25% percentile is 73.25.b) The 90% percentile is 92.82.c) 65% of X values are smaller than 83.85.d) 85% of X values are greater than 69.64.
The exam scores of a course follow a normal distribution with a mean of 78 and a standard deviation of 11.a) We are interested in the probability of a student getting a C or better (score of 70 or
A company extracts oil at a rig where the monthly weight of oil follows a normal distribution with mean 10 tons and standard deviation of 1.2 tons. Any monthly weight falling below the 25th
Among residents of a region, 35% live in and around a big city. If 50 residents are chosen at random, the exact probability that no more than 19 live in and around the big city can be found to be
Suppose the owner of a store knows that 15% paying costumers buy clothing from a well-known brand. If he chooses 150 paying customers at random, what is the probability that no less than 45 customers
An investment company claims that only 10% of their portfolios give a negative return on investment in a 1-year span. You take a random sample of 150 of their portfolios and find that 20 had a
A company that develops motorbike batteries knows that 10% of the batteries are defective. 300 batteries are randomly sampled:a) Show that X = number of defective batteries out of 300 follows a
If X ∼ exp(1∕2), show thata) P(X > 1) = 0.61.b) P(X ≤ 0.5) = 0.22.c) P(0.5 ≤ X ≤ 1) = 0.17.d) The ‰ is 1.39.
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

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