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principles of managerial statistics
Questions and Answers of
Principles Of Managerial Statistics
Using the data “2014_Housing_Market_Analysis_Data_by_Zip_Code,” produce a scatterplot of “rental units affordable to average teacher” and “owner units affordable to average teacher” at
Recall that a categorical scale with no logical order is known as nominal scale. Explain why for such data, the mode can be used, but not the mean or median.
Suppose we choose 2 balls from a bin with 100 red balls, 100 blue balls, and 100 green balls. If we define R = a red ball is chosen, B = a blue ball is chosen, and G = a green ball is chosen,a) Write
Show that for two independent events A, B, P(B|A) = P(B).
Let A and B be any two events. Assuming P(A) > 0 and P(B) > 0:a) Prove that if A is an event that is independent of B, then A is independent of Bc. Must be proven GENERALLY (IN AN ABSTRACTWAY),
If P(A|B) > P(A), show that P(B|A) > P(B).
If a population follows a normal distribution with mean 10 and standard deviation 2, show thata) If X is the value of a randomly sampled observation from this population, it has an expected value of
Find the standard error of X̅ for each random sampling situation.a) σ = 6, n = 10b) σ = 6, n = 40c) σ = 6, n = 60d) Do you need to assume the population is normally distributed for the
The company BEEFJERK produces 100 g of beef jerky with a mean saturated fat of 10 g and a standard deviation of 0.5 g. Fora) One serving of 100 g, what is the expected value of X̅?b) One serving of
Given a normal population with mean 250 and standard deviation 10,a) Should P(X̅ ≤ 259) be greater or smaller than 0.5?b) For which sample size, n = 30 or n = 20 would P(X̅ ≤ 259)
According to the National Center for Education Statistics, the mean costs (fees, room, and board rates) for a four-year public university in the United States was $15 640 for the 2013–2014 academic
The kilowatt/hour (kWh) generated by a solar system of 12 panels from (12–1 p.m.), during the summer months, has a normal distribution with mean 2.25 and a standard deviation of 0.5. If 10 solar
State in which of these cases it is more reasonable to assume that X̅ follows a normal distribution and explain why or why nota) Sample of size 300 comes from a population with some unknown
Two of your employees are conducting statistical analysis. Each one is working with a random sample of 30. The first employee took the sample from a population with a symmetric distribution. The
Average commute times (in minutes) to work at locations across Oregon are found online. With the variable “COMMUTING TO WORK - Mean travel time to work (minutes),” in the file
A machine produces bolts for construction. The length of the bolts has an expected value of 5 in and a variance of 0.05 in. A random sample of 100 bolts is taken.a) What is the mean (expected value)
If π = 0.20, find the mean and the standard error of p̂ whena) n = 100b) n = 200c) n = 50
Free-throw proportion in basketball is8 the number of free throws made divided by the number of attempts. A player has a 0.86 career free-throw proportion. Explain why any free-throw proportion
Determine if normality can be assumed for p̂ whena) n = 25, π = 0.50b) n = 100, π = 0.97c) n = 1000, π = 0.001d) n = 1500, π = 0.21
An employee from a company’s new products department is conducting research on the number of product parts a machine can assemble in an hour. Unbeknown to him, the population distribution is left
For a population with population mean 50 and standard deviation 7,a) If the population is normally distributed, which sample size would lead to the smallest variance for X̅, n = 100 or n = 300?b) If
A December 2017 CNN article established that life expectancy in the United States, on average, was 78.6. Assume that the standard deviation of life expectancy was 12 years. If a random sample that
It has been stated that the standard error of X̅ is σ/√n. This assumes that the population is infinite. If n is a significant proportion of the population size, N, a finite population correction
A company is about to randomly choose customers to fill surveys evaluating the company’s service. One of the questions asks whether customers will use or recommend the company’s services in the
Mention at least three properties that we want an estimator to have.
Construct a confidence interval for μ using each random sample. Assume X̅ is normally distributed.a) x̅ = 58.5, n = 55, σ = 9.2, 99% confidence.b) x̅ = 11.11, n = 150, σ = 1.25, 90%
In each case, state whether the interpretation of a confidence interval is correct or incorrect. If incorrect, explain why.a) There is a 99% probability that the true mean repair cost for a machine
A 90% confidence interval is built for the population mean using 32 observations.a) How likely is it that the confidence interval includes the sample mean?b) How likely is it that the confidence
A study of the effects of running on a random sample of adults found a 95% confidence interval for the true mean heart rate to be (68.74, 111.14), using a normal approximation procedure (the Z
According to www.fueleconomy.gov, a random sample of seven 2016 Subaru Forester AWD2.5 L, 4 cyl, automatic cars gave a mean of 26.4miles per gallon (MPG). Assume MPG for this vehicle follow a normal
The weight of Holstein cows in a farm has a standard deviation of 66.70 pounds. A random sample of 50 cattle has a mean weight of 1420.90 pounds.a) Why can we assume that the sample mean follows a
A random sample of 40 grass-fed beef prices in the United States gave an average of $3.70 (per pound). If the prices are not highly skewed and historically the standard deviation is $0.70,a)
Show that for a 99% confidence interval, zα∕2 = 2.576.
In the past, a car company had to face a burst of bad publicity when faulty brake parts led to car accidents. They would like to ensure their new car models do not have similar problems. To do so,
A solar power company must determine the sample size to infer on the mean utility bill of residents. From previous studies, it was established that the population standard deviation is 40
A university is concerned with its student’s first year mean GPA. They implement new guidelines in the hopes of improving the overall students performance. To verify the guidelines’
To construct a 99% confidence interval on the MPG of a type of vehicle, researchers are debating whether they want a margin of error of 1, or of 2.a) Which margin of error will require a bigger
If t follows a t-distribution with 10 degrees of freedom, and Z a standard normal distribution, determine which probability will be greater (no computation is necessary).a) P(Z > 1.12) versus P(t
A company is in the early stages of developing an eco-friendly laundry machine that will use less water than the competition. A team has conducted a study to determine the mean number of gallons of
Construct a confidence interval for μ using each random sample. Assume a normally distributed population.a) x̅ = 79.3, n = 12, s = 9.2, 95% confidence.b) x̅ = 5.81, n = 20, s = 0.75, 90%
As an owner of a local accounting firm, you would like to know the mean tax refund people get in your town. This way you can advertise how customers can benefit from your services to get a better
Suppose authorities in Chicago, Illinois, would like to estimate the mean number of days to complete graffiti removal request from private property owners. Weekly mean number of days to complete
In an analysis of a random sample of 75 claims to an insurance company, collision repair costs are found to have a mean of $1386. From previous studies, the standard deviation is known to be $735.a)
According to official Kansas City January 2018 records, the monthly average pay of 16 Accountant II positions was $4053. The minimum pay was $3353 and maximum pay was $5757. Someone would like to use
Construct a confidence interval for π using each random sample and a normal approximation.a) x = 34, n = 55, 95% confidence.b) x = 17, n = 149, 90% confidence.c) x = 214, n = 555, 99% confidence.d)
In Problem 9.24, check for each case if the conditions for a normal approximation hold.Data from in Problem 9.24Construct a confidence interval for π using each random sample and a normal
A 95% confidence interval is built for the population proportion using 200 observations.a) If the chosen confidence level was instead 90%at the same sample size, which confidence interval would be
Suppose the administration at a local university claims that 65% of their college graduates obtain jobs no longer than a month after graduation. For 150 randomly chosen college graduates of the
From the 2013 New York Youth Behavioral Risk Survey, we can be 95% confident that the proportion of youth who drank five or more alcoholic drinks in the past 30 days is between (0.098, 0.118). If a
According to the CDC, in 2015, of 208 595 kids younger than six years old tested for lead in the blood in Massachusetts, 5889 had levels between 5 and 9 μg/dl. Calculate a 95% confidence interval
A reporter wants to gauge the opinion of college undergraduates about legalizing marijuana,a) Using pn = 0.65 (from a similar study), and a 95% confidence level, determine what the sample size is for
Researchers studying criminal domestic violence rates per 100 000 people in country X took a random sample of 39 cities with at least 250 000 residents. Below, a graphical summary is presented.a)
A nonprofit wishes to build a 95% confidence interval on the proportion of uninsured Americans in the United States. In 2010, 16% of Americans had no insurance. In 2016, it was 8.6%.a) If the
To infer on the proportion of new business that fail within five years, it is found that a random sample of 1877 businesses is needed. The boss considers this sample size to be too large and suggests
After much effort, you are convincing your “old school” boss to construct a confidence interval as part of the decision-making process for a new customer service program. Regarding the confidence
A company will conduct an experiment to determine whether the mean time it takes to make a type of earring is within a certain limit. Assuming that the times to make the earrings have a standard
A university is concerned with the second-year student’s mean GPA. They implement new guidelines in the hopes of improving the overall students’ performance. To verify the guidelines’
The Southern California authorities are 95% confident that the rate of people killed in traffic accidents in 2010 was between (4.27, 4.89). Find the point estimate of the rate of people killed.
As part of the decision about opening a new store, the management of a company wanted to infer about the average amount of daily sales the store would have. They knew for a fact that the standard
The owner of an oil change shop would like to know the mean time it takes to do an oil change at the shop. He takes a random sample of 16 cars that were serviced and finds a sample average of 20.5
Current weekly sales of regular ground coffee at a supermarket average 354 pounds and vary according to a normal distribution. The store wants to reduce the price to sell more ground coffee. After
An indicator of the reliability of an estimate is known as the Relative Standard Errors (RSE). RSE = s.e.∕estimate × 100, where s.e. is the standard error of the estimate. In 2013, with 95%
A manufacturer of automobile tires claims that the average number of trouble-free miles given by one line of tires made by his company is 45 000 miles. When 16 randomly picked tires were tested, the
Construct a 99% confidence interval for the true proportion of adolescents in California who consumed five or more servings of fruits and vegetables a day, when in a 2012 random sample of 1143
The spokesperson of a company claims that over 88% of Americans either own a drone or know somebody who does. In a random survey of 1036 Americans, 856 said they or someone they know owned a drone.
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.
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