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Statistics Principles And Methods 7th Edition Richard A. Johnson, Gouri K. Bhattacharyya - Solutions

Find the area under the standard normal curve over the interval (a) z = -.44 to z = .44 (b) z = -1.33 to z = 1.33 (c) z = .40 to z = 2.03 (d) z = 1.405 to z = 2.306 (interpolate)
Identify the z values in the following diagrams of the standard normal distribution (interpolate, as needed).
Identify the z values in the following diagrams of the standard normal distribution (interpolate, as needed).
Determine the following probabilities from the curve f(x) diagrammed in Exercise 6.1 (a). (a) P[0 < X < .5] (b) P[.5 < X < 1] (c) P[1.0 < X < 2] (d) P[X = 1]
For a standard normal random variable Z, find (a) P[Z < .62] (b) P[Z < -.62] (c) P[Z > 1.59] (d) P[Z > -1.59] (e) P[ -1.3 < Z < 2.61 ] (f) P[.08 < Z < .8] (g) P[-1.62 < Z < -.34] (h) P[\Z\ < 1.65]
Find the z value in each of the following cases, (a) P[Z < z] = .1762 (b) P[Z > z] = .10 (c) P[-z < Z < z] = .954 (d) P[-.6 < Z < z] = .50
Find the quartiles of the standard normal distribution.
Find (a) P[Z < .33]. (b) The 33 rd percentile of the standard normal distribution. (c) P[Z < .97]. (d) The 97th percentile of the standard normal distribution.
Find (a) P[Z < .46]. (b) The 46th percentile of the standard normal distribution. (c) P[Z < .85]. (d) The 85th percentile of the standard normal distribution.
Records suggest that the normal distribution with mean 50 and standard deviation 9 is a plausible model for a measurement of the amount of suspended solids (ppm) in river water. Find(a) P[X < 46.4](b) P[X < 57.2](c) P[X > 57.2](d) P[X > 60.8](e) P[33.8 < X < 64.4](f) P[52.5 < X
Data suggests that the normal distribution with mean 13.0 and standard deviation 2.4 is a plausible model for the length (feet) of adult anaconda snakes. Find(a) P[X < 10.4](b) P[X < 17.8](c) P[X > 17.8](d) P[X > 16.72](e) P[ 10.24 < X < 18.4](f) P[14.8 < X < 17.2]
Referring to Exercise 6.25, find b such that (a) P[X < b] = .975 (b) P[X > b] = .025 (c) P[X < b] = .305
Referring to Exercise 6.26, find b such that (a) P[X < b] = .7995 (b) P[X > b] = .002 (c) P[X < b] = .015
Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 500 and a standard deviation of 100. Find the probability that a student will score: (a) Over 650. (b) Less than 250. (c) Between 325 and 675.
For the curve f(x) graphed in Exercise 6.1(c), which of the two intervals [0 < X < .5] or [1.5 < X < 2] is assigned a higher probability?
It is reasonable to model the distribution that produced the College Qualification Test (CQT) data in Exercise 2.22 as a normal distribution with mean 150 and standard deviation 25.4. (a) What is the probability of a new student scoring above 195? (b) What score has probability .15 of being
According to the children's growth chart that doctors use as a reference, the heights of two-year-old boys are nearly normally distributed with a mean of 34.5 inches and a standard deviation of 1.4 inches. If a two-year-old boy is selected at random, what is the probability that he will be between
The time it takes a symphony orchestra to play Beethoven's Ninth Symphony has a normal distribution with a mean of 64.3 minutes and a standard deviation of 1.15 minutes. The next time it is played, what is the probability that it will take between 62.5 and 67.7 minutes?
The weights of apples served at a restaurant are normally distributed with a mean of 5 ounces and standard deviation of 1.2 ounces. What is the probability that the next person served will be given an apple that weighs less than 4 ounces?
The diameter of hail hitting the ground during a storm is normally distributed with a mean of .5 inch and a standard deviation of .1 inch. What is the probability that: (a) A hailstone picked up at random will have a diameter greater than .71 inch? (b) Two hailstones picked up in a row will have
Refer to Exercise 6.10 where, according to current U.S. Census Bureau data, the heights of 20-to 29-year-old women can be well approximated by a normal distribution with mean 64.4 inches and standard deviation 3.0 inches. (a) What is the probability that the height of a randomly selected woman 20
Suppose the contents of bottles of water coming off a production line have a normal distribution with mean 9.1 ounces and standard deviation .1 ounce. (a) If every bottle is labeled 9 ounces, what proportion of the bottles contain less than the labeled amount? (b) If only 2.5% of the bottles exceed
The time for an emergency medical squad to arrive at the sports center at the edge of town is distributed as a normal variable with p. = 17 minutes and a = 3 minutes. (a) Determine the probability that the time to arrive is: (i) More than 22 minutes. (ii) Between 13 and 21 minutes. (iii) Between
It is reasonable to model the distribution that produced the lizards' speed test in Exercise 2.19 as normal distribution with mean 1.7 m/s and standard deviation .57 m/s. Find the probability that the speed of a new lizard (a) Will exceed 2.5 m/s. (b) Will be less than 1.5. (c) Will lie between 1.5
Let the number of successes X have a binomial distribution with n = 25 and p = .6(a) Find the exact probabilities of each of the following:X = 17 11 < X < 18 11 < X < 18(b) Apply the normal approximation to each situation in part (a).
Let the number of successes X have a binomial distribution with n = 25 and p = .4 (a) Find the exact probability of each of the following:X = 11 6 < X < 12 6 < X < 12(b) Apply the normal approximation to each situation in part (a).
A study by the National Endowment of the Arts revealed that 19.7% of adults age 18-24 played a musical instrument in the past 12 months. Suppose that is still the current rate. What is the normal approximation to the probability, that in a random sample of 100 adults age 18-24, the number who
A recent study reported that 54% of the adults in the United States drink at least one cup of coffee a day. Suppose that this is still the current rate. What is the normal approximation to the probability that, in a random sample of 1000 adults, the number that drink at least one cup a day will
State whether or not the normal approximation to the binomial is appropriate in each of the following situations (a) n = 90, P = .24 (b) n = 100, P = .03 (c) ft = 120, P = .98 (d) n = 61, P = .40
State whether or not the normal approximation to the binomial is appropriate in each of the following situations. (a) n = 500, P = .23 (b) n = 10, P = .40 (c) n = 300, P = .02 (d) n = 150, P = .97 (e) n = 100, P = .71
Copy Figure 16 and add the standard score scale z = (x - np)/√np(1 - p) underneath the x-axis for n = 5, 12, 25. Notice how the distributions center on zero and most of the probability lies between z = -2 and z = 2.
The median age of residents of the United States is 37.2 years. If a survey of 200 residents is taken, approximate the probability that at least 110 will be under 37.2 years of age.
The unemployment rate in a city is 7.9%. A sample of 300 persons is selected from the labor force. Approximate the probability that (a) Less than 18 unemployed persons are in the sample. (b) More than 30 unemployed persons are in the sample.
A survey reports that 96% of the people think that violence has increased in the past five years. Out of a random sample of 50 persons, 48 expressed the opinion that citizens have become more violent in the past five years. Does the normal approximation seem appropriate for X = the number of
According to the U.S. Statistical Abstract 2012, about 27.2% of persons age 18-24 participated in charity work in the past year. Among a sample of 64 persons in this age group, find the probability that 20 or more participated in charity work.
Determine the median and the quartiles for the curve depicted in Exercise 6.1(c).
The weekly amount spent by a small company for in-state travel has approximately a normal distribution with mean $1450 and standard deviation $220. What is the probability that the actual expenses will exceed $1560 in 20 or more weeks during the next year?
With reference to Exercise 6.50, calculate the probability that the actual expenses would exceed $ 1500 for between 18 and 24 weeks, inclusive during the next year.
In a large midwestern university, 30% of the students live in apartments. If 200 students are randomly selected, find the probability that the number of them living in apartments will be between 55 and 70 inclusive.
According to a study of mobility, 26% of U.S. residents in the age group 20 to 24 years moved to different housing in 2010 from where they lived in 2009. (Based on Statistical Abstract of the U.S. 2012 Table 30.) If the same percentage holds today, give the approximate probability that in a random
Suppose that 20% of the trees in a forest are infested with a certain type of parasite.(a) What is the probability that, in a random sample of 300 trees, the number of trees having the parasite will be between 49 and 71 inclusive?(b) After sampling 300 trees, suppose that 72 trees are found to have
Normal-scores plot. Use a computer program to make a normal-scores plot for the volume of timber data in Table 4. (Courtesy of Professor Alan Ek) Comment on the departure from normality displayed by the normal-scores plot.TABLE 4Volume of timber in cordsWe illustrate a normal-scores plot using
Use MINITAB or another package program to make a normal-scores plot of the malt extract data in Table D.8 of the Data Bank.
The MINITAB computer language makes it possible to easily transform data. With the data already set in column 1, the commandswill place the natural logarithm loge, x in C2, ˆšx in C3, and x1/14 in C4. Normal-scores plots can then be constructed as in Exercise 6.55. Refer to the lightning
Determine the 15th percentile of the curve in Exercise 6.1(a).
Refer to the volume of timber data in Example 13. (a) Make a normal-scores plot of the original data. (b) Make a normal-scores plot of the fourth root of the data. (c) Compare the two plots and comment.
Determine (a) the median and (b) the quartiles for the distribution shown in the following illustration.
For X having the density in Exercise 6.61, find (a) P[X > .7] (b) P[.5 < X < .7] (c)P[.5 < X < .7]
In the context of the height of red pine seedlings presented at the front of the chapter, describe the reasoning that leads from a histogram to the concept of a probability density curve. (Think of successive histograms based on 100 heights, 500 heights, 1456 heights, and then an unlimited number.)
For a standard normal random variable Z, find (a) P[Z < 1.56] (b) P[Z > 1.245 ] (c) P[.61 < Z < 1.92] (d) P[-1.47 < Z < 1.055]
For the standard normal distribution, find the value z such that (a) Area to its left is .0838. (b) Area to its left is .047. (c) Area to its right is .2611. (d) Area to its right is .12.
Find the 20th, 40th, 60th, and 80th percentiles of the standard normal distribution.
If Z is a standard normal random variable, what is the probability that (a) Z exceeds .62? (b) Z lies in the interval (-1.40, 1.40)? (c) | Z | exceeds 3.0? (d) | Z | is less than 2.0?
According to Example 12, a normal distribution with mean 115 and standard deviation 22 hundredths of an inch describes variation in female salmon growth in freshwater. (a) If a newly caught female salmon has growth 108, what is the corresponding standardized score? (b) If a standardized score is
The bell-shaped histogram for the heights of three-year-old red pine seedlings on page 232 is consistent with the assumption of a normal distribution having mean = 280 and sd = 58 millimeters. Let X denote the height, at three years of age, of the next red pine that will be measured. Find (a) P[X <
If a student is more likely to be late than on time for the 1:20 PM history class: (a) Determine if the median of the student's arrival time distribution is earlier than, equal to, or later than 1:20 PM. (b) On the basis of the given information, can you determine if the mean of the student's
If X has a normal distribution with p = 100 and a = 5, find b such that (a) P[X < b] = .6700 (b) P[X > b] = .0110 (c) P[|X - 100| < b] = .966
Suppose that a student's verbal score X from next year's Graduate Record Exam can be considered an observation from a normal population having mean 499 and standard deviation 120. Find (a) P[X > 600] (b) 90th percentile of the distribution. (c) Probability that the student scores below 400.
The lifting capacities of a class of industrial workers are normally distributed with mean 65 pounds and standard deviation 8 pounds. What proportion of these workers can lift an 80-pound load?
The bonding strength of a drop of plastic glue is normally distributed with mean 100 pounds and standard deviation 8 pounds. A broken plastic strip is repaired with a drop of this glue and then subjected to a test load of 90 pounds. What is the probability that the bonding will fail?
The scores on an examination are normally distributed with mean p = 70 and standard deviation a = 8. Suppose that the instructor decides to assign letter grades according to the following scheme (left endpoint included). Scores Grade Less than 58...................... F 58 to
Suppose the duration of trouble-free operation of a new robotic vacuum cleaner is normally distributed with mean 750 days and standard deviation 100 days. (a) What is the probability that the vacuum cleaner will work for at least two years without trouble? (b) The company wishes to set the warranty
Suppose the amount of a popular sport drink in bottles leaving the filling machine has a normal distribution with mean 101.5 milliliters (ml) and standard deviation 1.6 ml. (a) If the bottles are labeled 100 ml, what proportion of the bottles contain less than the labeled amount. (b) If only 5% of
Suppose the amount of sun block lotion in plastic bottles leaving a filling machine has a normal distribution. The bottles are labeled 300 milliliters (ml) but the actual mean is 302 ml and the standard deviation is 2 ml. (a) What is the probability that an individual bottle will contain less than
Suppose the random variable X is normally distributed with mean μ and standard deviation σ. If Y is a linear function of X -that is, Y = a + bX, where a and b are constants-then V is also normally distributed with Mean = a + bμ sd = |b|σ For instance, if X is distributed as N(25, 2) and Y = 7 -
Let X denote the number of successes in n Bernoulli trials with a success probability of p. (a) Find the exact probabilities of each of the following: (i) X < 7 when n = 25, p = .4 (ii) 11 < X < 16 when n = 20, p = .7 (iii) X > 9 when n = 16, p = .5 (b) Use a normal approximation for each situation
Which of the distributions in Figure 3 are compatible with the following statements? (a) The first test was too easy because over half the class scored above the mean. (b) In spite of recent large increases in salary, half of the professional football players still make less than the average salary.
It is known from past experience that 7% of the tax bills are paid late. If 20,000 tax bills are sent out, approximate the probability that: (a) Less than 1350 are paid late. (b) 1480 or more are paid late.
A particular program, say, program A, previously drew 30% of the television audience. To determine if a recent rescheduling of the programs on a competing channel has adversely affected the audience of program A, a random sample of 400 viewers are asked whether or not they currently watch this
The number of successes X has a binomial distribution. State whether or not the normal approximation is appropriate in each of the following situations: (a) n = 400, p = .23 (b) n = 20, p = .03 (c) n = 90, p = .98.
Because 10% of the reservation holders are "no-shows," a U.S. airline sells 400 tickets for a flight that can accommodate 370 passengers. (a) Find the approximate probability that one or more reservation holders will not be accommodated on the flight. (b) Find the approximate probability of fewer
On a Saturday afternoon, 147 customers are observed during check-out and the number paying by card, credit or debit, is recorded. Records from the store suggest that 43% of customers pay by card. Approximate the probability that: (a) More than 60 will pay by card. (b) Between 60 and 70, inclusive,
In all of William Shakespeare's works, he used 884,6475 different words. Of these, 14,376 appeared only once. In 1985 a 429-word poem was discovered that may have been written by Shakespeare. To keep the probability calculations simple, assume that the choices between a new word and one from the
Referring to Exercise 6.55, use MINITAB or another package program to make a normal-scores plot of the computer anxiety scores in Table D.4 of the Data Bank.
Refer to Exercise 6.59 and to the yearly deaths due to lightening in Exercise 2.121. Make a normal-scores plot for the square root of the number of deaths. Comment on the agreement with the ideal straight-line pattern.
Find the standardized variable Z if X has (a) Mean 15 and standard deviation 4. (b) Mean 61 and standard deviation 9. (c) Mean 161 and variance 25.
Identify each of the following as either a parameter or a statistic. (a) Population standard deviation. (b) Sample interquartile range. (c) Population 20th percentile. (d) Sample first quartile. (e) Sample median.
Referring to Exercise 7.9, use a die to generate samples of size 3. Investigate the sampling distribution of the number of times a value 1 occurs in a sample of size 3.(a) Roll the die and assign X = 1 if 1 dot shows and X = 0, otherwise. Repeat until you obtain a total of 25 samples of size 3.
The population density function and that for the sampling distribution of X are shown in Figure 5. Identify which one is the sampling distribution and explain your answer.Figure 5 Two density functions. Exercise 7.11.
Refer to the monthly intersection accident data in Exercise 5.96. The data suggests that one plausible In Exercise 5.96 Refer to the monthly intersection accident data in Exercise 2.4. Considering an even longer record leads to a distribution for X = number of accidents in a month. Value
Refer to Exercise 7.13. Determine the standard deviation of for a random sample of size (a) 9. (b) 36 (c) 144. (d) How does quadrupling the sample size change the standard deviation of ?
Using the sampling distribution determined for = (X1 + X2)/2 in Exercise 7.5, verify that E[] = μ and sd() = σ/√2.
Using the sampling distribution determined for = (X1 + X2)/2 in Exercise 7.6, verify that E[] = μ and sd() = σ/√2.
Suppose the number of different computers used by a student last week has distributionValue Probability0..............................31............................. .42............................. .3Let X1 and X2 be independent and each have the same distribution as the population.(a) Determine
Identify the parameter, statistic, and population when they appear in each of the following statements. (a) During a recent year, forty-one different movies received the distinction of generating the most box office revenue for a weekend. (b) A survey of 400 minority persons living in Chicago
As suggested in Example 8, Chapter 6, the population of hours of sleep can be modeled as a normal distribution with mean 7.2 hours and standard deviation 1.3 hours. For a sample of size 4, determine the (a) Mean of X. (b) Standard deviation of X. (c) Distribution of X.
According to Example 12, Chapter 6, a normal distribution with mean 115 and standard deviation 22 hundredths of an inch describes the variation in female salmon growth in freshwater. For a sample of size 6, determine the (a) Mean of X. (b) Standard deviation of X. (c) Distribution of X.
A population has distributionValue Probability0.............................72............................ .14............................ .2Let X1 and X2 be independent and each have the same distribution as the population.(a) Determine the missing elements in the table for the sampling
Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.4 ounces and standard deviation .4 ounce. (a) If every can is labeled 32 ounces, what proportion of the cans have contents that weigh less than the labeled amount? (b) If two packages are randomly
Suppose the amount of a popular sport drink in bottles leaving the filling machine has a normal distribution with mean 101.5 milliliters (ml) and standard deviation 1.6 ml.(a) If the bottles are labeled 100 ml, what proportion of the bottles contain less than the labeled amount?(b) If four bottles
The distribution of personal income of full-time retail clerks working in a large eastern city has p = $51,000 and a = $5000.(a) What is the approximate distribution for X based on a random sample of 100 persons?(b) Evaluate P[ > 51,500].
The result of a recent survey suggests that one plausible population distribution, for X = number of persons with whom an adult discusses important matters, can be modeled as a population having mean μ = 2.0 and standard deviation σ = 2.0. A random sample of size 100 is obtained.(a) What can you
The lengths of the trout fry in a pond at the fish hatchery are approximately normally distributed with mean 3.4 inches and standard deviation .8 inch. Three dozen fry are netted and their lengths measured. (a) What is the probability that the sample mean length of the 36 netted trout fry is less
The heights of male students at a university have a nearly normal distribution with mean 70 inches and standard deviation 2.8 inches. If 5 male students are randomly selected to make up an intramural basketball team, what is the probability that the heights of the team averages over 72.0 inches?
According to the growth chart that doctors use as a reference, the heights of two-year-old boys are normally distributed with mean 34.5 inches and standard deviation 1.3 inches. For a random sample of 6 two-year-old boys, find the probability that the sample mean is between 34.1 and 35.2 inches.
Data obtained from asking the wrong questions at the wrong time or in the wrong place can lead to misleading summary statistics. Explain why the following collection procedures are likely to produce useless data. (a) To evaluate the number of students who are employed at least part time, the
The weight of an almond is normally distributed with mean .05 ounce and standard deviation .015 ounce. Find the probability that a package of 100 almonds weighs between 4.8 and 5.3 ounces. That is, find the probability that is between .048 and .053 ounce.
Refer to Table 5 on page 288.(a) Calculate the sample median for each sample.(b) Construct a frequency table and make a histogram.(c) Compare the histogram for the median with that given in Figure 3 for the sample mean. Does your comparison suggest that the sampling distribution of the mean or
The number of days, X, that it takes the post office to deliver a notarized letter cross-country between City A and City B has the probability distribution align="center">(a) Find the expected number of days and the standard deviation of the number of days.(b) A company in City A sends a
The number of complaints per day, X, received by a cable TV distributor has the probability distribution align="center">(a) Find the expected number of complaints per day.(b) Find the standard deviation of the number of complaints.(c) What is the probability distribution of total number of

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