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statistics for engineers and scientists
Statistics For Engineers And Scientists 6th Edition William Navidi - Solutions
Find a \(95 \%\) confidence interval for the mean difference between the year in which the maximum temperature was recorded and the year in which the minimum temperature was recorded.
Refer to Exercise 13. Are the results of the confidence interval consistent with the hypothesis that temperatures have been rising over time? Explain.Data From Exercise 13:Find a \(95 \%\) confidence interval for the mean difference between the year in which the maximum temperature was recorded and
Find the following values.a. \(\chi_{12,025}^{2}\)b. \(\chi_{12,975}^{2}\)c. \(\chi_{5,005}^{2}\)d. \(\chi_{5,995}^{2}\)e. \(\chi_{22,1}^{2}\)f. \(\chi_{22,9}^{2}\)
Following are interest rates (annual percentage rates) for a 30-year fixed-rate mortgage from a sample of lenders in Colorado on November 9, 2021. Assume that the population is normally distributed.Construct a 95\% confidence interval for the population variance \(\sigma^{2}\).The chi-square
The pressure of air (in \(\mathrm{MPa}\) ) entering a compressor is measured to be \(X=8.5 \pm 0.2\), and the pressure of the air leaving the compressor is measured to be \(Y=21.2 \pm 0.3\). The intermediate pressure is therefore measured to be \(P=\sqrt{X Y}=13.42\). Assume that \(X\) and \(Y\)
The mass (in \(\mathrm{kg}\) ) of a soil specimen is measured to be \(X=1.18 \pm 0.02\). After the sample is dried in an oven, the mass of the dried soil is measured to be \(Y=0.85 \pm 0.02\). Assume that \(X\) and \(Y\) come from normal populations and are unbiased. The water content of the soil
A student measures the acceleration \(A\) of a cart moving down an inclined plane by measuring the time \(T\) that it takes the cart to travel \(1 \mathrm{~m}\) and using the formula \(A=2 / T^{2}\). Assume that \(T=0.55 \pm 0.01 \mathrm{~s}\), and that the measurement \(T\) comes from a normal
The initial temperature of a certain container is measured to be \(T_{0}=20^{\circ} \mathrm{C}\). The ambient temperature is measured to be \(T_{a}=4^{\circ} \mathrm{C}\). An engineer uses Newton's law of cooling to compute the time needed to cool the container to a temperature of \(10^{\circ}
Refer to the data set gravity.csv.a. Generate 1000 bootstrap samples from these data. Find the 2.5 and 97.5 percentiles.b. Compute a \(95 \%\) bootstrap confidence interval for the mean, using method 1 as described on page 395 .c. Compute a \(95 \%\) bootstrap confidence interval for the mean,
Refer to the data set pit.csv.a. Generate 1000 bootstrap samples from the pit depths at four weeks and 75\% humidity. Find the 2.5 and 97.5 percentiles.b. Compute a \(95 \%\) bootstrap confidence interval for the mean, using method 1 as described on page 395 .c. Compute a \(95 \%\) bootstrap
A sample of size 64 has standard deviation \(s=3.6\). Approximately how large a sample is needed so that a \(99 \%\) confidence interval will specify the mean to within \(\pm 1.0\) ?
Refer to Exercise 26.a. Generate 10,000 bootstrap samples from the data in Exercise 26. Find the bootstrap sample mean percentiles that are used to compute a \(99 \%\) confidence interval.b. Compute a \(99 \%\) bootstrap confidence interval for the mean compressive strength, using method 1 as
A sample of 50 copper wires had a mean resistance of \(1.03 \mathrm{~m} \Omega\) with a standard deviation of \(0.1 \mathrm{~m} \Omega\). Let \(\mu\) represent the mean resistance of copper wires of this type.a. Find the \(P\)-value for testing \(H_{0}: \mu \leq 1\) versus \(H_{1}: \mu>1\).b.
A sample of 65 electric motors had a mean efficiency of 0.595 with a standard deviation of 0.05 . Let \(\mu\) represent the mean efficiency of electric motors of this type.a. Find the \(P\)-value for testing \(H_{0}: \mu \geq 0.6\) versus \(H_{1}: \mu
In a test of corrosion resistance, a sample of \(60 \mathrm{In}\) coloy steel specimens were immersed in acidified brine for four hours, after which each specimen had developed a number of corrosive pits. The maximum pit depth was measured for each specimen. The mean depth was \(850 \mu
A process that manufactures steel bolts is supposed to be calibrated to produce bolts with a mean length of \(5 \mathrm{~cm}\). A sample of 100 bolts has a mean length of \(5.02 \mathrm{~cm}\). The population standard deviation is \(0.06 \mathrm{~cm}\). Let \(\mu\) be the mean length of bolts
Fill in the blank: In a test of \(H_{0}: \mu \geq 10\) versus \(H_{1}: \mu
An automotive engineer subjects a large number of brake pads to a stress test and measures the wear on each. The values obtained are \(\bar{X}=7.4 \mathrm{~mm}\) and \(\sigma_{\bar{X}}=0.2 \mathrm{~mm}\). Use this information to find the \(P\)-value for testing \(H_{0}: \mu=7.0\) versus \(H_{1}:
The following output (from \(\mathrm{R}\) ) presents the results of a hypothesis test for a population mean \(\mu\).a. Is this a one-tailed or a two-tailed test?b. What is the null hypothesis?c. What is the \(P\)-value?d. Assume the population standard deviation is \(\sigma=11.6189\) and the sample
The following output (from \(\mathrm{R}\) ) presents the results of a hypothesis test for a population mean \(\mu\).a. Is this a one-tailed or a two-tailed test?b. What is the null hypothesis?c. What is the \(P\)-value?d. Assume the population standard deviation is \(\sigma=1.6397\) and the sample
Scores on a certain IQ test are known to have a mean of 100 . A random sample of 60 students attend a series of coaching classes before taking the test. Let \(\mu\) be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if
The calibration of a scale is checked by weighing a standard \(10 \mathrm{~g}\) weight 100 times. Let \(\mu\) be the population mean reading on the scale, so that the scale is in calibration if \(\mu=10\). A test is made of the hypotheses \(H_{0}: \mu=10\) versus \(H_{1}: \mu eq 10\).Consider three
A sample of size \(n=100\) is used to test \(H_{0}: \mu \leq 20\) versus \(H_{1}: \mu>20\). The value of \(\mu\) will not have practical significance unless \(\mu>25\). The population standard deviation is \(\sigma=10\). The value of \(\bar{X}\) is 21 .a. Assume the sample size is \(n=100\).
A new method of postoperative treatment was evaluated for patients undergoing a certain surgical procedure. Under the old method, the mean length of hospital stay was 6.3 days. The sample mean for the new method was 6.1 days. A hypothesis test was performed in which the null hypothesis stated that
Erin computes a \(95 \%\) confidence interval for \(\mu\) and obtains (94.6, 98.3). Jamal performs a test of the hypotheses \(H_{0}: \mu=100\) versus \(H_{1}: \mu eq 100\) and obtains a \(P\)-value of 0.12 . Explain why they can't both be right.
A \(99 \%\) confidence interval for \(\mu\) is \((5.1,5.8)\). Someone wants to use the data from which this confidence interval was constructed to test \(H_{0}: \mu=6\) versus \(H_{1}: \mu eq 6\). The \(P\)-value will be i. greater than 0.01 ii. less than 0.01 iii. equal to 0.01
A shipment of fibers is not acceptable if the mean breaking strength of the fibers is less than \(50 \mathrm{~N}\). A large sample of fibers from this shipment was tested, and a \(98 \%\) lower confidence bound for the mean breaking strength was computed to be \(50.1 \mathrm{~N}\). Someone suggests
Refer to Exercise 23. It is discovered that the mean of the sample used to compute the confidence bound is \(\bar{X}=3.40\). Is it possible to determine whether \(P
Refer to Exercise 24. It is discovered that the standard deviation of the sample used to compute the confidence interval is 5 N5 N. Is it possible to determine whether P
The following output presents the results of a hypothesis test for a population mean \(\mu\).a. Can \(H_{0}\) be rejected at the \(5 \%\) level? How can you tell?b. Someone asks you whether the null hypothesis \(H_{0}: \mu=73\) versus \(H_{1}: \mu eq 73\) can be rejected at the \(5 \%\) level. Can
The General Social Survey asked a sample of adults how many siblings (brothers and sisters) they had \((X)\) and also how many children they had \((Y)\). We show results for those who had no more than 4 children and no more than 4 siblings. Assume that the joint probability mass function is given
Refer to Exercise 9.a. Find \(\mu_{X+Y}\).b. Find \(\sigma_{X+Y}\).c. Find \(P(X+Y=5)\).Data From Exercise 9:The General Social Survey asked a sample of adults how many siblings (brothers and sisters) they had \((X)\) and also how many children they had \((Y)\). We show results for those who had no
Refer to Exercise 9.a. Find the conditional probability mass function \(p_{Y \mid X}(y \mid 4)\).b. Find the conditional probability mass function \(p_{X \mid Y}(x \mid 3)\).c. Find the conditional expectation \(E(Y \mid X=4)\).d. Find the conditional expectation \(E(X \mid Y=3)\).Data From
Let \(a,b, c, d\) be any numbers with \(aIn other words, \(f(x, y)\) is constant on the rectangle \(aa. Show that \(k=\frac{1}{(b-a)(d-c)}\).b. Show that the marginal density of \(X\) is \(f_{X}(x)=\) \(1 /(b-a)\) for \(ac. Show that the marginal density of \(Y\) is \(f_{Y}(y)=\) \(1 /(d-c)\) for
A calibration laboratory has received a weight that is labeled as \(1 \mathrm{~kg}\). It is weighed five times. The measurements are as follows, in units of micrograms above \(1 \mathrm{~kg}\) : 114.3, 82.6, 136.4, 126.8, 100.7.a. Is it possible to estimate the uncertainty in these measurements? If
A measurement of the diameter of a disk has an uncertainty of \(1.5 \mathrm{~mm}\). How many measurements must be made so that the diameter can be estimated with an uncertainty of only \(0.5 \mathrm{~mm}\) ?
Refer to Exercise 4. Assume that \(T=298.4 \pm 0.2 \mathrm{~K}\). Estimate \(V\), and find the relative uncertainty in the estimate.
A Bernoulli random variable has variance 0.21 . What are the possible values for its success probability?
Let \(X \sim \operatorname{Bin}(7,0.3)\). Finda. \(P(X=1)\)b. \(P(X=2)\)c. \(P(X4)\)e. \(\mu_{X}\)f. \(\sigma_{X}^{2}\)
Let \(X \sim \operatorname{Bin}(9,0.4)\). Finda. \(P(X>6)\)b. \(P(X \geq 2)\)c. \(P(2 \leq X
Find the following probabilities:a. \(P(X=2)\) when \(X \sim \operatorname{Bin}(4,0.6)\)b. \(P(X>2)\) when \(X \sim \operatorname{Bin}(8,0.2)\)c. \(P(X \leq 2)\) when \(X \sim \operatorname{Bin}(5,0.4)\)d. \(P(3 \leq X \leq 5)\) when \(X \sim \operatorname{Bin}(6,0.7)\)
Several million lottery tickets are sold, and \(60 \%\) of the tickets are held by women. Five winning tickets will be drawn at random.a. What is the probability that three or fewer of the winners will be women?b. What is the probability that either two or three of the winners will be women?
A marketing manager samples 150 people and finds that 87 of them have made a purchase on the internet within the past month.a. Estimate the proportion of people who have made a purchase on the internet within the past month, and find the uncertainty in the estimate.b. Estimate the number of people
A quality engineer samples 100 steel rods made on mill \(A\) and 150 rods made on mill \(B\). Of the rods from mill \(\mathrm{A}, 88\) meet specifications, and of the rods from mill B, 135 meet specifications.a. Estimate the proportion of rods from mill \(\mathrm{A}\) that meet specifications, and
A commuter must pass through three traffic lights on the way to work. For each light, the probability that it is green upon arrival is 0.6. The lights are independent.a. What is the probability that all three lights are green?b. The commuter goes to work five days per week. Let \(X\) be the number
A distributor receives a large shipment of components. The distributor would like to accept the shipment if \(10 \%\) or fewer of the components are defective and to return it if more than \(10 \%\) of the components are defective. The distributor decides to sample 10 components and will return the
Let \(X \sim \operatorname{Bin}(n, p)\), and let \(Y=n-X\). Show that \(Y \sim \operatorname{Bin}(n, 1-p)\).
Let \(X \sim\) Poisson(4). Finda. \(P(X=1)\)b. \(P(X=0)\)c. \(P(X1)\)e. \(\mu_{X}\)f. \(\sigma_{X}\)
The number of pits in a corroded steel coupon follows a Poisson distribution with a mean of 6 pits per \(\mathrm{cm}^{2}\). Let \(X\) represent the number of pits in a \(1 \mathrm{~cm}^{2}\) area. Finda. \(P(X=8)\)b. \(P(X=2)\)c. \(P(X1)\)e. \(\mu_{X}\)f. \(\sigma_{X}\)
The number of large packages delivered by a courier service follows a Poisson distribution with a rate of 5 per day. Let \(X\) be the number of large packages delivered on a given day. Finda. \(P(X=6)\)b. \(P(X \leq 2)\)c. \(P(5
To estimate the concentration of particles in a certain suspension, a chemist withdraws \(3 \mathrm{~mL}\) of the suspension and counts 48 particles. Estimate the concentration in particles per \(\mathrm{mL}\), and find the uncertainty in the estimate.
To estimate the concentration of a certain type of bacterium in a wastewater sample, a microbiologist puts a \(0.5 \mathrm{~mL}\) sample of the wastewater on a microscope slide and counts 39 bacteria. Estimate the concentration of bacteria, per \(\mathrm{mL}\), in this wastewater, and find the
Grandpa is trying out a new recipe for raisin bread. Each batch of bread dough makes three loaves, and each loaf contains 20 slices of bread.a. If he puts 100 raisins into a batch of dough, what is the probability that a randomly chosen slice of bread contains no raisins?b. If he puts 200 raisins
Dad and Grandpa are each baking chocolate chip cookies. Each gives you two cookies. One of Dad's cookies has 14 chips in it and the other has Grandpa's cookies have 6 and 8 chips.a. Estimate the mean number of chips in one of Dad's cookies.b. Estimate the mean number of chips in one of Grandpa's
Twenty-five automobiles have been brought in for service. Fifteen of them need tuneups and ten of them need new brakes. Nine cars are chosen at random to be worked on. What is the probability that three of them need new brakes?
In a lot of 15 truss rods, 12 meet a tensile strength specification. Four rods are chosen at random to be tested. Let \(X\) be the number of tested rods that meet the specification.a. Find \(P(X=3)\).b. Find \(\mu_{X}\).c. Find \(\sigma_{X}\).
Among smartphone users, \(40 \%\) use a case but no screen protector, \(10 \%\) use a screen protector but no case, \(45 \%\) use both a case and a screen protector, and \(5 \%\) use neither a case nor a screen protector. Twenty smartphone users are sampled at random. Let \(X_{1}, X_{2}\), \(X_{3},
Let \(X \sim \operatorname{Geom}(p)\), let \(n\) be a non-negative integer, and let \(Y \sim \operatorname{Bin}(n, p)\). Show that \(P(X=n)=\) \((1 / n) P(Y=1)\).
Find the area under the normal curvea. To the left of \(z=0.56\).b. Between \(z=-2.93\) and \(z=-2.06\).c. Between \(z=-1.08\) and \(z=0.70\).d. Outside \(z=0.96\) to \(z=1.62\).
If \(X \sim N(2,9)\), computea. \(P(X \geq 2)\)b. \(P(1 \leq X
A process manufactures ball bearings with diameters that are normally distributed with mean \(25.1 \mathrm{~mm}\) and standard deviation \(0.08 \mathrm{~mm}\).a. What proportion of the diameters are less than \(25.0 \mathrm{~mm}\) ?b. Find the 10th percentile of the diameters.c. A particular ball
Depths of pits on a corroded steel surface are normally distributed with mean \(822 \mu \mathrm{m}\) and standard deviation \(29 \mu \mathrm{m}\).a. Find the 10th percentile of pit depths.b. A certain pit is \(780 \mu \mathrm{m}\) deep. What percentile is it on?c. What proportion of pits have
In a recent study, the Centers for Disease Control reported that diastolic blood pressures (in \(\mathrm{mmHg}\) ) of adult women in the United States are approximately normally distributed with mean 80.5 and standard deviation 9.9.a. What proportion of women have blood pressures lower than 70 ?b.
The lifetime of a light bulb in a certain application is normally distributed with mean \(\mu=1400\) hours and standard deviation \(\sigma=200\) hours.a. What is the probability that a light bulb will last more than 1800 hours?b. Find the 10th percentile of the lifetimes.c. A particular light bulb
Speeds of automobiles on a certain stretch of freeway at 11:00 PM are normally distributed with mean \(65 \mathrm{mph}\). Twenty percent of the cars are traveling at speeds between 55 and \(65 \mathrm{mph}\). What percentage of the cars are going faster than \(75 \mathrm{mph}\) ?
Scores on an exam were normally distributed. Ten percent of the scores were below 64 and \(80 \%\) were below 81 . Find the mean and standard deviation of the scores.
Let \(X \sim N\left(\mu, \sigma^{2}ight)\), and let \(Z=(X-\mu) / \sigma\). Use Equation (4.25) to show that \(Z \sim N(0,1)\).
Two resistors, with resistances \(R_{1}\) and \(R_{2}\), are connected in series. \(R_{1}\) is normally distributed with mean \(100 \Omega\) and standard deviation \(5 \Omega\), and \(R_{2}\) is normally distributed with mean \(120 \Omega\) and standard deviation \(10 \Omega\). Assume \(R_{1}\) and
The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution \(\left(1ight.\) mole \(=6.02 \times 10^{23}\) molecules \()\). If \(X\) is the molarity of a solution of sodium chloride \((\mathrm{NaCl})\), and \(Y\) is the molarity of a solution of sodium
The period \(T\) of a simple pendulum is given by \(T=\) \(2 \pi \sqrt{L / g}\) where \(L\) is the length of the pendulum and \(g\) is the acceleration due to gravity. Assume that \(g=\) \(9.80 \mathrm{~m} / \mathrm{s}^{2}\) exactly, and that \(L\), in meters, is lognormal with parameters
The volume of a cylinder is given by \(V=\pi r^{2} h\), where \(r\) is the radius of the cylinder and \(h\) is the height. Assume the radius, in \(\mathrm{cm}\), is lognormal with parameters \(\mu_{r}=1.6\) and \(\sigma_{r}^{2}=0.04\), the height, in \(\mathrm{cm}\), is lognormal with parameters
Refer to Exercise 5. Suppose 10 pendulums are constructed. Find the probability that 4 or more have periods greater than 3 seconds.Data From Exercise 5:The period \(T\) of a simple pendulum is given by \(T=\) \(2 \pi \sqrt{L / g}\) where \(L\) is the length of the pendulum and \(g\) is the
Refer to Exercise 6. Suppose 8 cylinders are constructed. Find the probability that fewer than 5 of them have volumes between 500 and \(800 \mathrm{~cm}^{3}\).Data From Exercise 6:The volume of a cylinder is given by \(V=\pi r^{2} h\), where \(r\) is the radius of the cylinder and \(h\) is the
A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with \(\mu=5\) and \(\sigma=0.5\). Let \(X\) be the strength of a randomly sampled specimen of this composite.a. If the claim is true, what is \(P(X
The distance between flaws on a long cable is exponentially distributed with mean \(12 \mathrm{~m}\).a. What is the value of the parameter \(\lambda\) ?b. Find the median distance.c. Find the standard deviation of the distances.d. Find the 65th percentile of the distances.
Refer to Exercise 2.a. Find the probability that there will be exactly 5 requests in a 2 -second time interval.b. Find the probability that there will be more than 1 request in a 1.5 -second time interval.c. Find the probability that there will be no requests in a 1-second time interval.d. Find the
Refer to Exercise 4.a. Find the probability that there are exactly 5 flaws in a \(50 \mathrm{~m}\) length of cable.b. Find the probability that there are more than two flaws in a \(20 \mathrm{~m}\) length of cable.c. Find the probability that there are no flaws in a \(15 \mathrm{~m}\) length of
A radioactive mass emits particles according to a Poisson process. The probability that no particles will be emitted in a two-second period is 0.5 .a. What is the probability that no particles are emitted in a four-second period?b. What is the probability that no particles are emitted in a
The lifetime of a transistor is exponentially distributed. The probability that the lifetime is greater than five years is 0.8 .a. What is the probability that the lifetime is greater than 15 years?b. What is the probability that the lifetime is less than 2.5 years?c. What is the mean lifetime?
A sample of 100 cars driving on a freeway during a morning commute was drawn, and the number of occupants in each car was recorded. The results were as follows:a. Find the sample mean number of occupants.b. Find the sample standard deviation of the number of occupants.c. Find the sample median
Five basketball players and 11 football players are working out in a gym. The mean height of the basketball players is \(77.6 \mathrm{in}\)., and the mean height of all 16 athletes is \(74.5 \mathrm{in}\). What is the mean height of the football players?
An insurance company examines the driving records of 100 policy holders. They find that 80 of them had no accidents during the past year, 15 had one accident, 4 had two, and 1 had three.a. Find the mean number of accidents.b. Find the median number of accidents.c. Which quantity is more useful to
Match each histogram to the boxplot that represents the same data set. 144 (a) e (b) X (2) (3) I +
In general a histogram is skewed to the left when the median is greater than the mean and to the right when the median is less than the mean. There are exceptions, however. Consider the following data set:0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 3a. Compute the mean and median.b. Based on the mean
Refer to the file lung.csv.a. Construct a histogram for the values of FEV1.b. Is the histogram symmetric, skewed to the left, or skewed to the right?c. Construct a boxplot for the values of FEV1.d. Are there any outliers in these data? If so, are they unusually large or unusually small
Refer to the file gravity.csv.a. Construct a histogram for the measurements of the acceleration due to gravity.b. Apart from outliers, is the histogram unimodal or bimodal?c. Construct a boxplot for the measurements of the acceleration due to gravity.d. How many outliers are in these data?Exercises
Refer to the file pit.csv.a. Consider the pits at 52 weeks duration. Construct comparative boxplots for the depths at \(40 \%\) and \(75 \%\) relative humidity.b. Using the boxplots, what differences can be seen in the distributions of depths at \(40 \%\) and \(75 \%\) relative humidity?Exercises
There are 15 numbers on a list, and the smallest number is changed from 12.9 to 1.29 .a. Is it possible to determine by how much the mean changes? If so, by how much does it change?b. Is it possible to determine the value of the mean after the change? If so, what is the value?c. Is it possible to
The probability that a bolt meets a strength specification is 0.87 . What is the probability that the bolt does not meet the specification?
According to a report by the Agency for Healthcare Research and Quality, the age distribution for people admitted to a hospital for an asthma-related illness was as follows.a. What is the probability that an asthma patient is between 18 and 64 years old?b. What is the probability that an asthma
A company audit showed that of all bills that were sent out, \(71 \%\) of them were paid on time, \(18 \%\) were paid up to 30 days late, \(9 \%\) were paid between 31 and 90 days late, and \(2 \%\) remained unpaid after 90 days. One bill is selected at random.a. What is the probability that the
In a certain community, \(28 \%\) of the houses have fireplaces and \(51 \%\) have garages. Is it possible to compute the probability that a randomly chosen house has either a fireplace or a garage? If so, compute the probability. If not, explain why not.
According to the National Health Statistics Reports, \(16 \%\) of American families have one child, and \(21 \%\) have two children. Is it possible to compute the probability that a randomly chosen family has either one or two children? If so, compute the probability. If not, explain why not.
Resistors manufactured by a certain process are labeled as having a resistance of \(5 \Omega\). A sample of 100 resistors is drawn, and 87 of them have resistances between 4.9 and \(5.1 \Omega\). True or false:a. The probability that a resistor has a resistance between 4.9 and \(5.1 \Omega\) is
License plates in a certain state consist of three letters followed by three digits.a. How many different license plates can be made?b. How many license plates are there that contain neither the letter " \(Q\) " nor the digit " 9 "?c. A license plate is drawn at random. What is the probability that
Joe, Megan, and Santana are salespeople. Their sales manager has 18 accounts and must assign six accounts to each of them. In how many ways can this be done?
Suppose that \(90 \%\) of bolts and \(85 \%\) of nails meet specifications. One bolt and one nail are chosen independently.a. What is the probability that both meet specifications?b. What is the probability that neither meets specifications?c. What is the probability that at least one of them meets
At a certain car dealership, \(20 \%\) of customers who bought a new vehicle bought an SUV, and 3\% of them bought a black SUV. Given that a customer bought an SUV, what is the probability that it was black?
At a certain college, \(30 \%\) of the students major in engineering, \(20 \%\) play club sports, and \(10 \%\) both major in engineering and play club sports. A student is selected at random.a. What is the probability that the student is majoring in engineering?b. What is the probability that the
Lorez and Felipe each fire one shot at a target. Lorez has probability 0.5 of hitting the target, and Felipe has probability 0.3 . The shots are independent.a. Find the probability that the target is hit.b. Find the probability that the target is hit by exactly one shot.c. Given that the target was
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