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principles of managerial statistics
Questions and Answers of
Principles Of Managerial Statistics
When X ∼ U(75,125). Show thata) P(75 ≤ X ≤ 100) = 0.5.b) P(80 ≤ X ≤ 111) = 0.62.c) P(X ≥ 112.5) = 0.25.d) P(X < 60) = 0.e) E(X) = 100.f) Var(X) = 208.33.
If X ∼ U(15, 50). Finda) P(15 ≤ X ≤ 25)b) P(20 ≤ X ≤ 30)c) P(X < 37)d) P(X ≤ 37)e) P(X > 42)f) E(X)g) Var(X)
Find the expected value and standard deviation of X for each case.a) U(10, 50)b) U(100,500)c) U(200,400)d) U(0,100)
If X ∼ U(15, 50), determine the value x such that it is the 75th percentile.
If X ∼ U(103,225), determine the value x such that only 5% of values of the random variable exceed it.
X ∼ U(0,800) has the same expected value as Y ∼ U(200,600). Check if P(X ≤ 250) = P(Y ≤ 250). Also check if Var(X) = Var(Y).
Assume the weight of cargo for a company truck follows a uniform distribution ranging between 300 and 450 pounds.a) What is the expected value of the weight of the cargo?b) What is the standard
Past records of the temperature in Miami show an average temperature, for the months from September to October, which follows a uniform distribution with temperatures between 82 and 87. Suppose that
Refer back to Figure 7.4. What do the values in the x axis of a normal probability density function represent? What do the values in the y axis represent? Density 100 120 Normal density 140 150
Suppose that Z follows an N(0, 1). In the following, state whether the probability is greater than 0.5, lower than 0.5, equal to 0.5, or if it is not possible to tell just by common sense, without
Z follows an N(0, 1). In the following, state whether the probability is greater than 0.5, lower than 0.5, equal to 0.5, or if it is not possible to tell just by common sense, without computing the
Z follows an N(0, 1). Show thata) P(Z < −1.57) = 0.058.b) P(Z ≥ 0.18) = 0.43.c) P(Z < −5.34) = 0.d) P(−0.12 < Z < 0.33) = 0.18.
Z follows an N(0, 1). In the following, state whether the given probability is correct or incorrect. If incorrect, explain why.a) P(Z ≥ 1.28) = 0.8997.b) P(Z < −0.11) = 0.4602.c) P(Z <
If Z follows an N(0, 1), compute the following probabilities:a) P(Z < 2.44).b) P(Z ≤ 2.44).c) P(Z ≥ 15.32).d) P(Z ≤ −0.15).e) P(Z ≥ −1.96).f) P(Z > −7.43).g) P(Z ≤ −9.32).h)
If Z follows an N(0, 1).a) Show that P(−3 ≤ Z ≤ 3) = 0.9997.b) Find P(−2 < Z < 2).c) Find P(−1 < Z < 1).d) Find P(−0.75 < Z < 0.75).
Find the z-value or z values:a) Such that it is the 25% percentile.b) Such that it is the 75% percentile.c) Such that at most 15% of z-scores are higher.d) Such that the area under the middle of the
In the following, without computing the actual probabilities, state whether the probability is greater than 0.5, lower than 0.5, equal to 0.5, or if it is not possible to tell just by common sense.
In the following, without computing the actual probabilities, state whether the probability is greater than 0.5, lower than 0.5, equal to 0.5, or if it is not possible to tell just by common sense.
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
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