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Statistics 13th Global Edition James T. McClave And Terry T Sincich - Solutions
Here are the raw data for the ANES unique group of widows with three or more kids at home:Number of days read newspaper per week: 3, 2, 1, 7, 1, 0, 0, 0, 0, 2, 2 Use these raw data to construct a 95% confidence interval.
Among those aged 17 to 34, does having a smartphone instead of a regular cell phone make one more likely to review news on the Internet? Using ANES data, select cases to look at this age group, and then get 95%confidence intervals on the Internet news variable for those who have smartphones and
According to the ANES, 22 of the 32 black respondents aged 17 to 20 have smart-phones. Build a 95% confidence interval with this information.
Run confidence intervals by state using the ANES Muslims feeling thermometer and report the 95% confidence intervals for the first five states: Alaska (AK), Alabama (AL), Arkansas (AR), Arizona (AZ), and California (CA). Explain why the confidence intervals differ in width for these states.
When someone rates a group at 10 on the ANES feeling thermometer, that’s a pretty serious sign of dislike. I make the claim that the population of African American, female strong Democrats aged 17 to 34 on average rate Republicans at a chilly 10 degrees. Is this possible? Test this claim.
how researchers used confidence intervals to study Uber and traffic fatalities
how a researcher used confidence intervals to study popular films
how to build and interpret confidence intervals
population claims and how to put them to the test
what the Central Limit Theorem is and why it is important
how to find and interpret the standard error of a sampling distribution
building a probability distribution of sample means
Learned how to find probabilities of discrete events by using the probability rules of Chapter 3. LO8
Discussed probability models (distributions) for discrete random variables in Chapter 4 Where We’re Going LO8
Develop the notion of a probability distribution for a continuous random variable. (5.1) LO8
Study several important types of continuous random LO8 variables and their probability models. (5.2–5.3, 5.6)
Introduce the normal probability distribution as one of the most useful distributions in statistics. (5.3–5.5) LO8
Super Weapons development—is the hit ratio optimized? LO8
Researchers at the University of Rochester studied the friction that occurs in the paper-feeding process of a photocopier and published their results in the Journal of Engineering for Industry. The friction coefficient, x, is a continuous random variable that measures the degree of friction between
An unprincipled used-car dealer sells a car to an unsuspecting buyer, even though the dealer knows that the car will have a major breakdown within the next 6 months. The dealer provides a warranty of 45 days on all cars sold. Let x represent the length of time until the breakdown occurs. Assume
True or False: The probability that the uniform random variable will assume a value in any interval of equal length is different for each interval. LO8
The uniform distribution is a __________ distribution. (Fill in the blank.) LO8
Refer to Exercise 5.3. Find the following probabilities: LO8a. P115 … x … 302b. P125 6 x 6 352c. P1x Ú 302d. P1x … 202e. P1x … 302f. P125.5 … x … 30.52
Suppose x is a random variable best described by a uniform probability distribution with c = 4 and d = 6. LO8a. Find f(x).b. Find the mean and standard deviation of x.c. Find P1m - s … x … m + s2.d. Find P1x 7 4.782.e. Find P14.4 … x … 5.72.f. Find P1x 6 42.
Refer to Exercise 5.5. Find the value of a makes each of the following probability statements true: LO8a. P1x Ú a2 = .5b. P1x … a2 = .2c. P1x … a2 = 0d. P14.5 … x … a2 = .5
The random variable x is best described by a uniform probability distribution with mean 100 and standard deviation 10. Findc, d, and f(x). Graph the probability distribution. LO8
Open the applet entitled Sample from a Population. On the pulldown menu to the right of the top graph, select Uniform. The box to the left of the top graph displays the population mean, median, and standard deviation.a. Run the applet for each available value of n on the pulldown menu for the
Reliability of a robotic device. The reliability of a piece of equipment is frequently defined to be the probability p that the equipment performs its intended function successfully for a given period under specific conditions (Render and Heizer, Principles of Operations Management, 1995).Because p
Find the probability that the standard normal random variable z falls between-1.33 and +1.33. LO8
Find the probability that a standard normal random variable exceeds 1.64; that is, find P1z 7 1.642. LO8
Find the probability that a standard normal random variable lies to the left of .67. LO8
Find the probability that a standard normal random variable exceeds 1.96 in absolute value. LO8
Find the value of z—call it z0—in the standard normal distribution that will be exceeded only 10% of the time. That is, find z0 such that P1z Ú z02 = .10. LO8
Find the value of z0 such that 95% of the standard normal z values lie between LO8-z0 and +z0; that is, find P1 -z0 … z … z02 = .95.
Suppose the scores x on a college entrance examination are normally distributed with a mean of 550 and a standard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90th percentile of the distribution. Find the minimum score
True or False: The normal distribution is a symmetric probability distribution. LO8
If x has a normal distribution with mean m and standard deviation s, find the mean of the random variable z = 1x - m2 >s. LO8
How do you transform a normal random variable to a standard normal random variable? LO8
Find each of the following probabilities for a standard normal random variable z: LO8a. P1z = 12b. P1z … 12c. P1z 6 12d. P1z 7 12e. P1 -1 … z … 12f. P1 -2 … z … 22 g. P1 -2.16 … z … .552 h. P1 -.42 6 z 6 1.962
Find the following probabilities for the standard normal random variable z: LO8a. P1z 7 1.462b. P1z 6 -1.562c. P1.67 … z … 2.412d. P1 -1.96 … z 6 -.332e. P1z Ú 02f. P1 -2.33 6 z 6 1.502 g. P1z Ú -2.332 h. P1z 6 2.332
Find a value z0 of the standard normal random variable z such that LO8a. P1z … z02 = .0401b. P1 -z0 … z … z02 = .95c. P1 -z0 … z … z02 = .90d. P1 -z0 … z … z02 = .8740e. P1 -z0 … z … 02 = .2967f. P1 -2 6 z 6 z02 = .9710 g. P1z Ú z02 = .5 h. P1z Ú z02 = .0057
Find a value z0 of the standard normal random variable z such that LO8a. P1z Ú z02 = .10b. P1z Ú z02 = .003c. P1z … z02 = .01d. P1z Ú z02 = .20e. P1z 7 z02 = .02
Suppose x is a normally distributed random variable with m = 11 and s = 2. Find each of the following: LO8a. P110 … x … 122b. P16 … x … 102c. P113 … x … 162d. P17.8 … x … 12.62e. P1x Ú 13.242f. P1x Ú 7.622
Suppose x is a normally distributed random variable with m = 40 and s = 10. Find a value x0 of the random variable x such that LO8a. P1x Ú x02 = .5b. P1x 6 x02 = .025c. P1x 7 x02 = .10d. P1x 7 x02 = .95
Refer to Exercise 5.32. Find x0 such that LO8a. 10% of the values of x are less than x0.b. 80% of the values of x are less than x0.c. 1% of the values of x are greater than x0.
Safety of underground tunnels. Research published in the journal Tunnelling and Underground Space Technology(July 2014) evaluated the safety of underground tunnels built in rigid soils. A Factor of Safety (FS), measured as the ratio of capacity over demand, was determined for three different areas
Ambulance response time. Ambulance response time is measured as the time (in minutes) between the initial call to emergency medical services (EMS) and when the patient is reached by ambulance. Geographical Analysis(Vol. 41, 2009) investigated the characteristics of ambulance response time for EMS
Alcohol, threats, and electric shocks. A group of Florida LO8 State University psychologists examined the effects of alcohol on the reactions of people to a threat (Journal of Abnormal Psychology, Vol. 107, 1998). After obtaining a specified blood alcohol level, the psychologists placed
subject. The mean and standard deviation of the startle responses were 37.9 and 12.4, respectively. Assume that the startle response x for a person with the specified blood alcohol level is approximately normally distributed.a. Find the probability that x is between 40 and 50 milli seconds.b. Find
The EPA mileage ratings on 100 cars, first presented in Chapter 2 (p. 71), are reproduced in Table 5.2. Recall that these data are saved in the EPAGAS file. Numerical and graphical descriptive measures for the data are shown on the MINITAB and SPSS LO8 printouts presented in Figure 5.21a–c.
How do you construct a normal probability plot of a data LO8 set from a normal population?
Give four methods for determining whether the sample LO8 data come from a normal population.
If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within the following intervals?a. m { .5sb. m { 2.5s LO8c. m { 1.25s
How do you use IQR to check that the data came from a standard normal distribution? LO8
Normal probability plots for three data sets are shown at LO8 the bottom of the page. Which plot indicates that the data are approximately normally distributed?
Examine the following sample data.32 48 25 135 53 37 5 39 213 165 109 40 1 146 39 25 21 66 64 57 197 60 112 10 155 134 301 304 107 82 35 81 60 95 401 308 180 3 200 59 LO8a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution.b. Find the values of
Examine the sample data in the next column.L05062a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution.b. Compute s for the sample data.5.9 5.3 1.6 7.4 8.6 3.2 2.1 4.0 7.3 8.4 5.9 6.7 4.5 6.3 6.0 9.7 3.5 3.1 4.3 3.3 8.4 4.6 8.2 6.5 1.1 5.0 9.4
Drug content assessment. Scientists at GlaxoSmithKline Medicines Research Center used high-performance liquid chromatography (HPLC) to determine the amount of drug in a tablet produced by the company (Analytical Chemistry, Dec. 15, 2009). Drug concentrations (measured as a percentage) for 50
One problem with any product that is mass produced (e.g., a graphing calculator)is quality control. The process must be monitored or audited to be sure that the output of the process conforms to requirements. One monitoring method is lot acceptance sampling, in which items being produced are
When will the normal distribution provide a reasonable approximation to the probabilities of most binomial LO8 events?
Can a binomial distribution with parameters n = 10 and p = .1 be well approximated by a normal distribution? LO8
Assume that x is a binomial random variable with n and p as specified in parts a–f that follow. For which cases would it be appropriate to use a normal distribution to approximate the binomial distribution? LO8a. n = 80, p = .03b. n = 100, p = .04c. n = 10, p = .6d. n = 500, p = .05e. n = 200, p
Assume that x is a binomial random variable with n = 20 and p = .5. Use Table I of Appendix B and the normal approximation to find the exact and approximate values, respectively, of the following probabilities: LO8a. P1x … 92b. P1x Ú 112c. P18 … x … 112
Assume that x is a binomial random variable with n = 1,200 and p = .50. Find each of the following probabilities: LO8a. P1x 7 6002b. P1589 … x 6 6002c. P1x 7 6552
Assume that x is a binomial random variable with n = 120 and p = .50. Use a normal approximation to find the following: LO8a. P1x … 552b. P160 … x … 802c. P1x Ú 582
Blood diamonds. According to Global Research News(Mar. 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds, i.e., diamonds mined to finance war or an insurgency. In a random sample of 1,000 rough diamonds purchased by a diamond buyer, let x be the number that are
Cesarean birth study. In Exercise 4.73 (p. 240), you learned that 75% of all births in a region occur by Cesarean section each year. In a random sample of 1,000 births this year, let x be the number that occur by Cesarean section. LO8a. Find the mean of x.b. Find the standard deviation of x.c. Find
Suppose the length of time (in hours) between emergency arrivals at a certain hospital is modeled as an exponential distribution with u = 2. What is the probability that more than 5 hours pass without an emergency arrival? LO8
A manufacturer of microwave ovens is trying to determine the length of warranty period it should attach to its magnetron tube, the most critical component in the oven. Preliminary testing has shown that the length of life (in years), x, of a magnetron tube has an exponential probability
What is the nature of the probability density function of an exponential random variable? LO8
The exponential distribution is often called the ________ distribution. (Fill in the blank.) LO8
Determine the value of e-a>u for each of the following cases: LO8a. u = 2, a = 2b. u = 2, a = 5c. u = .8, a = 6d. u = .4, a = .6
Suppose x has an exponential distribution with u = 1. Find the following probabilities:a. P1x 7 12b. P1x … 32 LO8c. P1x 7 1.52d. P1x … 52
Suppose x has an exponential distribution with u = 5. Find LO8 the following probabilities:a. P1x … 42b. P1x 7 52c. P1x … 22d. P1x 7 32
Earthquake recurrence in Iran. The Journal of Earthquake Engineering (Vol. 17, 2013) modeled the time x (in years)between major earthquakes occurring in the Iranian Plateau. One of the models considered had the following LO8 density function:f1x2 = .04e-.04x, x 7 0a. Find E(x). Interpret the
Product failure behavior. An article in Hotwire (Dec.2002) discussed the length of time till failure of a product produced at Hewlett-Packard. At the end of the product’s lifetime, the time till failure is modeled using an exponential distribution with mean 500 thousand hours. In reliability
Identify the type of continuous random variable—uniform, normal, or exponential—described by each of the following probability density functions: LO8a. f1x2 = 1e-x>82 >8, x 7 0b. f1x2 = 1>30, 10 6 x 6 40c. f1x2 =e-.531x - 122>742 722p
Use probability to make an inference about a population from data in an observed sample
Use probability to measure the reliability of the inference
Develop the notion of a random variable (4.1)
Learn that many types of numerical data are observed values of discrete random variables (4.1)
Learn the probabilistic properties of discrete random variables (4.2–4.3)
Study several important types of discrete random variables and their probability models (4.4–4.6)
Probability in a reverse Cocaine Sting:Was Cocaine really Sold? LO9
Refer to Example 4.2. A second random variable of interest is the amount x of pesticide (in milligrams per liter) found in the monthly sample of discharge waters from the same chemical company. What values can this random variable assume? LO9
Define a discrete random variable. LO9
Define a continuous random variable. LO9
Nutrition. Give an example of a discrete random variable of interest to a nutritionist. LO9
Physics. Give an example of a discrete random variable of interest to a physicist. LO9
Medical. Give an example of a discrete random variable of interest to a doctor in a hospital. LO9
Artist. Give an example of a discrete random variable of interest to an artist. LO9
Recall the experiment of tossing two coins (p. 213), and let x be the number of heads observed. Find the probability associated with each value of the random variable x, assuming that the two coins are fair. LO9
A drought is a period of abnormal dry weather that causes serious problems in the farming industry of the region. University of Arizona researchers used historical annual data to study the severity of droughts in Texas (Journal of Hydrologic Engineering, Sept./Oct. 2003). The researchers showed
How do you represent the probability distribution of a random variable denoting the number of heads when an unbiased coin tossed once? LO9
Consider the following probability distribution: LO9 x: -5 -2 0 1 p(x) .1 .2 .3 .4a. List the values that x may assume.b. What is the probability that x is greater than 0?c. What is the probability that x = -2?
Explain why each of the following is or is not a valid probability distribution for a discrete random variable x: LO9a. x 0 1 2 3 p(x) .2 .3 .3 .2b. x -2 -1 0 p(x) .25 .50 .20c. x 4 9 20 p(x) -.3 1.0 .3d. x 2 3 5 6 p(x) .15 .20 .40 .35
The random variable x has the following discrete probability distribution: LO9 x: 5 6 7 8 9 p(x:) .2 .3 .2 .1 .2 Since the values that x can assume are mutually exclusive events, the event 5x … 76 is the union of three mutually exclusive events:5x = 56 ∪ 5x = 66 ∪ 5x = 76a. Find P1x … 72.b.
The random variable x has the discrete probability distribution shown here: LO9 x: -4 -3 -2 -1 0 p(x:) .10 .15 .40 .30 .05a. Find P1x … -12.b. Find P1x 7 -12.c. Find P1x 6 02.d. Find P1x 6 -22.e. Find P1 -4 6 x 6 -12.f. Find P1x 6 -32.
Downloading apps to your cell phone. According to a study, nearly 40% of adult cell phone owners have downloaded an application (“app”) to their cell phone. The accompanying table gives the probability distribution for x, the number of apps used at least once a week by cell phone owners who
Controlling the water hyacinth. An insect that naturally feeds on the water hyacinth, one of the world’s worst aquatic weeds, is the delphacid. Female delphacids lay anywhere from one to four eggs onto a water hyacinth blade. The Annals of the Entomological Society of America(Jan. 2005) published
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