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statistics

Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions

Consider the binomial experiment with n = 300 and p = 0.2. a. Set up, but do not evaluate, the probability expression for 75 or fewer successes in the 300 trials. b. Use a computer or calculator to find P(x < 75) using the binomial probability function. c. Use a computer or calculator to find P(x <
Find the following areas under the standard normal curve. a. To the right of z = 3.18 P(z > 3.18) b. To the right of z = 1.84 P(z > 1.84) c. To the right of z = 0.75 P(z > 0.75)
A test-scoring machine is known to record an incorrect grade on 5% of the exams it grades. Find, by the appropriate method, the probability that the machine records a. exactly 3 wrong grades in a set of 5 exams. b. no more than 3 wrong grades in a set of 5 exams. c. no more than 3 wrong grades in a
A company asserts that 80% of the customers who purchase its special lawn mower will have no repairs during the first two years of ownership. Your personal study has shown that only 70 of the 100 lawn mowers in your sample lasted the two years without repair expenses. What is the probability of
It is believed that 58% of married couples with children agree on methods of disciplining their children. Assuming this to be the case, what is the probability that in a random survey of 200 married couples, we would find a. exactly 110 couples who agree? b. fewer than 110 couples who agree? c.
It turns out that making a lot of money doesn’t necessarily make you sexy. In a poll conducted by Salary.com, firefighters hosed down the competition and won the title of “sexiest job” with 16% of the votes. Suppose you randomly select 50 adults. Use the normal approximation to the binomial
National Coffee Dr-inking Trends is “the publication” in the coffee industry. Each year it tracks consumption patterns in a wide variety of situations and categories and has done so for over five decades. A recent edition says that 39% of the total coffee drinkers age 18 years and over have
Apparently playing video games, watching TV, and instant messaging friends isn’t relaxing enough. In a poll from Yesawich, Pepperdine, Brown and Russell found that the vast majority of children say they “need” a vacation. One-third of the children polled said they helped research some aspect
Infant-mortality rates are often used to assess quality of life and adequacy of health care. The rate is based on the number of deaths of infants under 1 year old in a given year per 1000 live births in the same year. Listed here are the infant-mortality rates, to the nearest integer, in eight
A large sample of lenses was randomly selected and evaluated for a particular lens dimension. It was then compared to its specification range of nominal (0.000) ± 0.030 units. One hundred ten lenses were evaluated. Data were coded in two ways and are shown below:Source: Courtesy of Bausch &
Assume that the distribution of data in Exercise 6.137 was exactly normally distributed, with a mean of 0.00 and a standard deviation of 0.020. a. Find the bounds of the middle 95% of the distribution. b. What percent of the data is actually within the interval found in part a? c. Using z-scores,
a. Find the area under the standard normal curve to the left of z = 0 P(z< 0) b. Find the area under the standard normal curve to the right of z = 0 P(z> 0)
Find the area under the standard normal curve between - 1.39 and the mean, P(_1.39
Find the area under the standard normal curve between z = -1.83 and z = 1.23, P(-1.83 < z < 1.23).
Find the area under the standard normal curve between z = -2.46 and z = 1.46, P(-2.46 < z < 1.46).
Find the area under the standard normal curve that corresponds to the following z-values. a. Between 0 and 1.55 b. To the right of 1.55 c. To the left of 1.55 d. Between -1.55 and 1.55
Examine the intelligence quotient, or IQ, as it is defined by the formula: Intelligence Quotient = 100 × (Mental Age/Chronological Age) Justify why it is reasonable for the mean to be 100.
Find the probability that a piece of data picked at random from a normal population will have a standard score (z) that lies a. between 0 and 0.74. b. to the right of 0.74. c. to the left of 0.74. d. between -0.74 and 0.74.
Find the following areas under the normal curve. a. To the right of z = 0.00 b. To the right of z = 1.05 c. To the right of z = -2.30 d. To the left of z = 1.60 e. To the left of z = -1.60
Find the probability that a piece of data picked at random from a normally distributed population will have a standard score that is a. less than 3.00. b. greater than -1.55. c. less than -0.75. d. less than 1.24. e. greater than -1.24.
Find the following: a. P(0.00 < z < 2.35) b. P(-2.10 < z < 2.34) c. P(z > 0.13) d. P(z < 1.48)
Find the following: a. P(-2.05 < z < 0.00) b. P(-1.83 < z < 2.07) c. P(z < -1.52) d. P(z < -0.43)
Find the following: a. P(0.00 < z < 0.74) b. P(-1.17 < z < 1.94) c. P(z > 1.25) d. P(z < 1.75)
Find the following: a. P(—3.05 < z < 0.00) b. P(—2.43 < z < 1.37) c. P(z < —2.17) d. d. P(z > 2.43)
Find the area under the normal curve that lies between the following pairs of z-values: a. z = —1.20 to z = —0.22 b. z = —1.75 to z = —1.54 c. z = 1.30 to z = 2.58 d. z = 0.35 to z = 3.50
Percentage, proportion, or probability-identify which is illustrated by each of the following statements. a. One-third of the crowd had a clear view of the event. b. Fifteen percent of the voters were polled as they left the voting precinct. c. The chance of rain during the day tomorrow is 0.2.
Find the probability that a piece of data picked at random from a normal population will have a standard score (z) that lies between the following pairs of z-values: a. to z = - 2.75 z = -1.38 b. to z = 0.67 z = 2.95 c. to z = - 2.95 z = -1.18
Find the z-score for the standard normal distribution shown in each of the following diagrams.
Find the z-score for the standard normal distribution shown in each of the following diagrams.
Find the standard score, z, shown in each of the following diagrams.
Find the standard score, z, shown in each of the following diagrams.
Assuming a normal distribution, what is the z-score associated with the 1st quartile? The 2nd quartile? The 3rd quartile?
a. Find the standard z-score such that 80% of the distribution is below (to the left of) this value. b. Find the standard z-score such that the area to the right of this value is 0.15. c. Find the two z-scores that bound the middle 50% of a normal distribution.
Applet Exercise demonstrates that probability is equal to area under a curve. Given that college students sleep an average of 7 hours per night, with a standard deviation equal to 1.7 hours, use the scroll bar in the applet to find: a. P(a student sleeps between 5 and 9 hours) b. P(a student
Skillbuilder Applet Exercise demonstrates the effects that the mean and standard deviation have on a normal curve. a. Leaving the standard deviation at 1, increase the mean to 3. What happens to the curve? b. Reset the mean to 0 and increase the standard deviation to 2. What happens to the
Given that x is a normally distributed random variable with a mean of 60 and a standard deviation of 10, find the following probabilities. a. P(x > 60) b. P(60 < x < 72) c. P(57 < x < 83) d. P(65 < x < 82) e. P(38 < x < 78) f. P(x < 38)
Given that x is a normally distributed random variable with a mean of 28 and a standard deviation of 7, find the following probability a. P(x < 28) b. P(28 < x < 38) c. P(24 < x < 40) d. P(30 < x < 45) e. P(19 < x < 35) f. P(x < 48)
As shown in Example 6.8, IQ scores are considered normally distributed, with a mean of 100 and a standard deviation of 16. a. Find the probability that a randomly selected person will have an IQ score between 100 and 120. b. Find the probability that a randomly selected person will have an IQ score
a. Describe the distribution of the standard normal score, z. b. Why is this distribution called standard normal?
Based on a survey conducted by Greenfield Online, 25 to 34-year-olds spend the most each week on fast food. The average weekly amount of $44 was reported in a May 2009 USA Today Snapshot. Assuming that weekly fast food expenditures are normally distributed with a standard deviation of $14.50, what
Depending on where you live and on the quality of the day care, costs of day care can range from $3000 to $15,000 a year (or $250 to $1250 a month) for one child, according to the Baby Center. Day care centers in large cities such as New York and San Francisco are notoriously expensive. Suppose
According to Collegeboard.com [www.college- board.com/] the national average salary for a plumber as of 2007 is $47,350. If we assume that the annual salaries for plumbers are normally distributed with a standard deviation of $5250, find the following: a. What percentage earn below $30,000? b. What
According to the Federal Highway Administration’s 2006 highway statistics, the distribution of ages for licensed drivers has a mean of 47.5 years and a standard deviation of 16.6 years [www.fhwa.dot.gov]. Assuming the distribution of ages is normally distributed, what percentage of the drivers
There is a new working class with money to burn, according to the USA Today March 1, 2005, article “New ‘gold-collar’ young workers gain clout.” “Gold-collar” is a subset of blue-collar workers, defined by researchers as those working in fast food and retail jobs, or as security guards,
Findings from a survey of American adults conducted by Yankelovich Partners for the International Bottled Water Association indicate that Americans on the average drink 6.1 8-ounce servings of water a day [www.pangaeawater.com/]. Assuming that the number of 8-ounce servings of water is
As shown in Example 6.12, incomes of junior executives are normally distributed with a standard deviation of $3828. a. What is the mean for the salaries of junior executives, if a salary of $62,900 is at the top end of the middle 80% of incomes? b. With the additional information learned in part a,
According to ACT, results from the 2008 ACT test-ing found that students had a mean reading score of 21.4 with a standard deviation of 6.0. Assuming that the scores are normally distributed, a. find the probability that a randomly selected student had a reading ACT score less than 20. b. find the
On a given day, the number of square feet of office space available for lease in a small city is a normally dis-tributed random variable with a mean of 750,000 square feet and a standard deviation of 60,000 square feet. The number of square feet available in a second small city is normally
A brewery’s filling machine is adjusted to fill quart bottles with a mean of 32.0 oz of ale and a variance of 0.003. Periodically, a bottle is checked and the amount of ale is noted. a. Assuming the amount of fill is normally distributed, what is the probability that the next randomly checked
Using the standard normal curve and z: a. Find the minimum score needed to receive an A if the instructor in Example 6.11 said the top 15% were to get A’s. b. Find the 25th percentile for IQ scores in Example 6.10. c. If SAT scores are normally distributed with a mean of 500 and a standard
Final averages are typically approximately normally distributed with a mean of 72 and a standard deviation of 12.5. Your professor says that the top 8% of the class will receive an A; the next 20%, a B; the next 42%, a C; the next 18%, a D; and the bottom 12%, an F. a. What average must you exceed
A radar unit is used to measure the speed of auto-mobiles on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a mean of 62 mph. a. Find the standard deviation of all speeds if 3% of the automobiles travel faster than 72 mph. b. Using the
The weights of ripe watermelons grown at Mr. Smith’s farm are normally distributed with a standard deviation of 2.8 lb. Find the mean weight of Mr. Smith’s ripe watermelons if only 3% weigh less than 15 lb.
A machine fills containers with a mean weight per container of 16.0 oz. If no more than 5% of the containers are to weigh less than 15.8 oz, what must the standard deviation of the weights equal? (Assume normality.)
“On-hold” times for callers to a local cable television company are known to be normally distributed with a standard deviation of 1.3 minutes. Find the average caller “on-hold” time if the company maintains that no more than 10% of callers have to wait more than 6 minutes.
The data below are the net weights (in grams) for a sample of 30 bags of M&€™s. The advertised net weight is 47.9 grams per bag.The FDA requires that (nearly) every bag contain the advertised weight; otherwise, violations (less than 47.9 grams per bag) will bring about mandated fines.
The extraction force required to remove a cork from a bottle of wine has a normal distribution with a mean of 310 Newtons and a standard deviation of 36 Newtons. a. The specs for this variable, given in Applied Example 6.13, were “300 N + 100 N/-150 N” Express these specs as an interval. b.
The diameter of each cork, as described in Applied Example 6.13, is measured in several places and an average diameter is reported for the cork. The average diameter has a normal distribution with a mean of 24.0 mm and standard deviation of 0.13 mm. a. The specs for this variable, given in Applied
a. Generate a random sample of 100 data from a normal distribution with mean 50 and standard deviation 12. b. Using the random sample of 100 data found in part a and the technology commands for calculating ordinate values on page 284, find the 100 corresponding y values for the normal distribution
Find the area under the normal curve that lies to the left of the following z-values a. z = - 1.30. b. z = - 2.56. c. z = - 3.20. d. z = - 0.64.
Use a computer or calculator to find the probability that one randomly selected value of x from a normal distribution, with mean 584.2 and standard deviation 37.3, will have a value a. less than 525. b. between 525 and 590. c. of at least 590. d. Verify the result using Table 3. e. Explain any
Using the z(a) notation (identify the value of a used within the parentheses), name each of the standard normal variable z€™s shown in the following diagrams
Using the z(a) notation (identify the value of a used within the parentheses), name each of the standard normal variable z€™s shown in the following diagrams.
Using the z(a) notation (identify the value of a used within the parentheses), name each of the standard normal variable z€™s shown in the following diagrams.
Using the z(a) notation (identify the value of a used within the parentheses), name each of the standard normal variable z’s shown in the following diagrams
Draw a figure of the standard normal curve showing: a. Z(0.15) b. Z(0.82)
Draw a figure of the standard normal curve showing: a. Z(0.04) b. Z(0.94)
We are often interested in finding the value of z that bounds a given area in the right-hand tail of the normal distribution, as shown in the accompanying figure. The notation z(a) represents the value of z such that P(z > Z(a)) = a. Find the following: z (0.025) b. z(0.05) c. z(0.01)
We are often interested in finding the value of z that bounds a given area in the left-hand tail of the normal distribution, as shown in the accompanying figure. The notation z(a) represents the value of z such that P(z > z(a)) = a. Find the following: a. z(0.98) b. z(0.80) c. z(0.70)
Use Table 4A, Appendix B, and the symmetry property of normal distributions to find the following values of z. a. z(0.05) b. z(0.01) c. z(0.025) d. z(0.975) e. z(0.98)
Using Table 4A and the symmetry property of the normal distribution, complete the following charts of z-scores. The area given in the tables is the area to the right under the normal distribution in the figures.a. z-scores associated with the right-hand tail: Given the area A, find z(A).b. z-scores
Using Table 4B, find the z-scores that bound the middle 0.80 of the normal distribution. Verify the z-scores using Table 4A.
Using Table 4B, find the z-scores that bound the middle 0.98 of the normal distribution. Verify the z-scores using Table 4A.
Using Table 4B, complete the following chart of z-scores that bound a middle area of a normal distribution.
a. Find the area under the normal curve for z between z(0.95) and z(0.025). b. Find z(0.025) - z(0.95).
The z notation, z (a), combines two related concepts, the z-score and the area to the right, into a mathematical symbol. Identify the letter in each of the following as being a z-score or an area, and then with the aid of a diagram explain what both the given number and the letter represent on the
Find the probability that a piece of data picked at random from a normal population will have a standard score (z) that lies to the left of the following z-values a. z = 2.10 b. z = 1.20 c. z = 3.26 d. z = 0.71
Understanding the z notation, z(a), requires us to c. z(100 — 001) d. z (0.025) — z (0.975) know whether we have a z-score or an area. Each of the following expressions uses the z notation in a variety of ways, some typical and some not so typical. Find the value asked for in each of the
Find the values np and nq (recall: q = 1 - p) for a binomial experiment with n = 100 and p = 0.02. Does this binomial distribution satisfy the rule for normal approximation? Explain.
In which of the following binomial distributions does the normal distribution provide a reasonable approximation? Use computer commands to generate a graph of the distribution and compare the results to the “rule of thumb.” State your conclusions. a. n = 10, p = 0.3 b. n = 100, p = 0.005 c. n
In order to see what happens when the normal approximation is improperly used, consider the binomial distribution with n = 15 and p = 0.05. Since np = 0.75, the rule of thumb (np > 5 and nq > 5) is not satisfied. Using the binomial tables, find the probability of one or fewer successes and compare
Find the normal approximation for the binomial probability P(x = 6), where n = 12 and p = 0.6. Compare this to the value of P(x = 6) obtained from Table 2.
Find the normal approximation for the binomial probability P(x = 4, 5), where n = 14 and p = 0.5. Compare this to the value of P(x = 4, 5) obtained from Table 2.
Find the normal approximation for the binomial probability P(x < 8), where n = 14 and p = 0.4. Compare this to the value of P(x < 8) obtained from Table 2.
Find the normal approximation for the binomial probability P(x > 9), where n = 13 and p = 0.7. Compare this to the value of P(x > 9) obtained from Table 2.
Referring to Example 6.21 (p. 302): a. Calculate P(x < 3|B(25, 3 )). b. How good was the normal approximation? Explain.
Melanoma is the most serious form of skin cancer and is increasing at a rate higher than any other cancer in the United States. If it is caught in its early stage, the 5-year survival rate for patients on average is 98% in the United States. What is the probability that 235 or more of some group of
Suppose a random sample of 100 ages was taken from the 2000 census distribution.a. How would you describe the €œages€ sample data above graphically? Construct the graph. b. Using the graph that you constructed in part a, describe the shape of the distribution of the sample
Considering the population of five equally likely integers in Example 7. 2:a. Verify m and s for the population in Example 7. 2.
In reference to Applied Example 7. 3 on page 316: a. Explain why the numerical values on this table do not form a sampling distribution. b. Explain how this repeated gathering of data differs from the idea of repeated sampling to gather information about a sampling distribution.
From the table of random numbers in Table 1 in Appendix B, construct another table showing 20 sets of 5 randomly selected single-digit integers. Find the mean of each set (the grand mean) and compare this value with the theoretical population mean, m, using the absolute difference and the % error.
a. Using a computer or a random number table, simulate the drawing of 100 samples, each of size 5, from the uniform probability distribution of single-digit integers, 0 to 9. b. Find the mean for each sample. c. Construct a histogram of the sample means. (Use integer values as class midpoints.)
a. Using a computer or a random number table, simulate the drawing of 250 samples, each of size 18, from the uniform probability distribution of single-digit integers, 0 to 9. b. Find the mean for each sample. c. Construct a histogram of the sample means. d. Describe the sampling distribution
a. Use a computer to draw 200 random samples, each of size 10, from the normal probability distribution with mean 100 and standard deviation 20. b. Find the mean for each sample. c. Construct a frequency histogram of the 200 sample means. d. Describe the sampling distribution shown in the
a. Use a computer to draw 500 random samples, each of size 20, from the normal probability distribution with mean 80 and standard deviation 15. b. Find the mean for each sample. c. Construct a frequency histogram of the 500 sample means. d. Describe the sampling distribution shown in the
a. Click €œ1€ for €œ# Samples.€ Note the four data values and their mean. Change €œslow€ to €œbatch€ and take at least 1000 samples using the €œ500€ for €œ# Samples.€b. What
a. Change the €œ# Observations per sample€ to €œ4.€ Using batch and 500, take 1000 samples of size 4.
a. What is the total measure of the area for any probability distribution? b. Justify the statement “ becomes less variable as n increases.”
a. What numerical statistics would you use to describe the “ages” sample data in Exercise 7.1? Calculate those statistics. According to the 2000 census (2010 census is not complete), 275 million Americans have a mean age of 36.5 years and a standard deviation of 22.5 years. b. How well do the
If a population has a standard deviation s of 25 units, what is the standard error of the mean if samples of size 16 are selected? Samples of size 36? Samples of size 100?

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