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mathematics
statistics
Fundamentals Of Statistics 4th Edition Michael Sullivan III - Solutions
The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 100 and standard deviation 15. (a) What is the probability that a randomly selected test taker will score above 125? (b) What is the probability that a randomly selected test taker will score below 90? (c)
According to major league baseball rules, the ball must weigh between 5 and 5.25 ounces. A factory produces baseballs whose weights are approximately normally distributed, with mean 5.11 ounces and standard deviation 0.062 ounce. (a) What proportion of the baseballs produced by this factory are
According to a Gallup poll, 46% of Americans 18 years old or older stated that they had read at least six books (fiction and nonfiction) within the past year. You conduct a random sample of 250 Americans 18 years old or older.(a) Verify that the conditions for using the normal distribution to
In 1798, Henry Cavendish obtained 27 measurements of the density of Earth, using a torsion balance. The following data represent his estimates, given as a multiple of the density of water. Is it reasonable to conclude that the sample data come from a population that is normally distributed?
According to a USA Today “Snapshot,” 20% of adults surveyed do their most creative thinking while driving. You conduct a survey of 250 adults and find that 30 do their most creative thinking while driving.(a) Compute the probability that, in a random sample of 250 adults, 30 or fewer do their
A continuous random variable X is uniformly distributed with 0 ≤ X ≤ 20. (a) Draw a graph of the uniform density function. (b) What is P(0 ≤ X ≤ 5)? (c) What is P(10 ≤ X ≤ 18)?
List the properties of the normal density curve.
Use the ï¬gure to answer the questions that follow:(a) What is µ? (b) What is σ? (c) Suppose that the area under the normal curve to the left of x = 10 is 0.9332. Provide two interpretations for this area. (d) Suppose that the area under the normal curve between x =
Draw a standard normal curve and shade the area to the right of z = 2.04. Then find the area of the shaded region.
Find the z-scores that separate the middle 88% of the data from the area in the tails of the standard normal distribution.
Find the value of z0.04.
(a) Draw a normal curve with µ = 20 and σ = 3. (b) Shade the region that represents P(22 ≤ X ≤ 27) and find the probability.
Suppose that the talk time on the Apple iPhone is approximately normally distributed with mean 7 hours and standard deviation 0.8 hour. (a) What proportion of the time will a fully charged iPhone last at least 6 hours? (b) What is the probability a fully charged iPhone will last less than 5
The waist circumference of males 20 to 29 years old is approximately normally distributed, with mean 92.5 cm and standard deviation 13.7 cm. (a) Use the normal model to determine the proportion of 20- to 29-year-old males whose waist circumference is less than 100 cm. (b) What is the probability
Suppose the scores earned on Professor McArthur’s third statistics exam are normally distributed with mean 64 and standard deviation 8. Professor McArthur wants to curve the exam scores as follows: The top 6% get an A, the next 14% get a B, the middle 60% get a C, the bottom 6% fail, and the rest
In a poll conducted by the Gallup organization, 16% of adult, employed Americans were dissatisfied with the amount of their vacation time. You conduct a survey of 500 adult, employed Americans.(a) Approximate the probability that exactly 100 are dissatisfied with their amount of vacation time.(b)
A continuous random variable X is uniformly distributed with 10 ≤ X ≤ 50. (a) Draw a graph of the uniform density function. (b) What is P(20 ≤ X ≤ 30)? (c) What is P(X < 15)?
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x = 0) or up to 30 minutes late (x = 30), with all intervals of equal time between x = 0 and x = 30
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x = 0) or up to 30 minutes late (x = 30), with all intervals of equal time between x = 0 and x = 30
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x = 0) or up to 30 minutes late (x = 30), with all intervals of equal time between x = 0 and x = 30
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x = 0) or up to 30 minutes late (x = 30), with all intervals of equal time between x = 0 and x = 30
The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Draw the graph of the uniform density function. (b) What is the probability of generating a number between 0 and
The reaction time X (in minutes) of a certain chemical process follows a uniform probability distribution with 5 ≤ X ≤ 10. (a) Draw the graph of the density curve. (b) What is the probability that the reaction time is between 6 and 8 minutes? (c) What is the probability that the reaction time
One graph in the ï¬gure represents a normal distribution with mean µ = 10 and standard deviation σ = 3. The other graph represents a normal distribution with mean µ = 10 and standard deviation σ = 2. Determine which graph is which and explain how you
One graph in the ï¬gure at the top of the next column represents a normal distribution with mean µ = 8 and standard deviation σ = 2. The other graph represents a normal distribution with mean µ = 14 and standard deviation σ = 2. Determine which graph
Draw a normal curve with µ = 30 and σ = 10. Label the mean and the inflection points.
Draw a normal curve with µ = 50 and σ = 5. Label the mean and the inflection points.
Monthly charges for cell phone plans in the United States are normally distributed with mean µ = +62 and standard deviation σ = +18. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of plans that charge less than $44. (c) Suppose the area
The lives of refrigerators are normally distributed with mean µ = 14 years and standard deviation σ = 2.5 years. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of refrigerators that last for more than 17 years. (c) Suppose the area under
The birth weights of full-term babies are normally distributed with mean µ = 3400 grams and σ = 505 grams. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of full-term babies who weigh more than 4410 grams. (c) Suppose the area under the
The heights of 10-year-old males are normally distributed with mean µ = 55.9 inches and σ = 5.7 inches. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of 10-year-old males who are less than 46.5 inches tall. (c) Suppose the area under the
The lengths of human pregnancies are normally distributed with µ = 266 days and σ = 16 days.(a) The ï¬gure represents the normal curve with µ = 266 days and σ = 16 days. The area to the right of x = 280 is 0.1908. Provide two interpretations of this
Elena conducts an experiment in which she ï¬lls up the gas tank on her Toyota Camry 40 times and records the miles per gallon for each ï¬ll-up. A histogram of the miles per gallon indicates that a normal distribution with a mean of 24.6 miles per gallon and a standard
In the game of golf, distance control is just as important as how far a player hits the ball. Michael went to the driving range with his range ï¬nder and hit 75 golf balls with his pitching wedge and measured the distance each ball traveled (in yards). He obtained the following
The following frequency distribution represents the heights (in inches) of 80 randomly selected 5-year-old females.(a) Use MINITAB or some other statistical software to construct a relative frequency histogram. Comment on the shape of the distribution. Draw a normal density curve on the relative
Determine the area under the standard normal curve that lies to the left of (a) z = -2.45 (b) z = -0.43 (c) z = 1.35 (d) z = 3.49 Find the indicated areas. Be sure to draw a standard normal curve and shade the area that is to be found.
Determine the area under the standard normal curve that lies to the left of (a) z = -3.49 (b) z = -1.99 (c) z = 0.92 (d) z = 2.90 Find the indicated areas. Be sure to draw a standard normal curve and shade the area that is to be found.
Determine the area under the standard normal curve that lies to the right of (a) z = -3.01 (b) z = -1.59 (c) z = 1.78 (d) z = 3.11 Find the indicated areas. Be sure to draw a standard normal curve and shade the area that is to be found.
Determine the area under the standard normal curve that lies to the right of (a) z = -3.49 (b) z = -0.55 (c) z = 2.23 (d) z = 3.45 Find the indicated areas. Be sure to draw a standard normal curve and shade the area that is to be found.
Determine the area under the standard normal curve that lies between (a) z = -2.04 and z = 2.04 (b) z = -0.55 and z = 0 (c) z = -1.04 and z = 2.76 Find the indicated areas. Be sure to draw a standard normal curve and shade the area that is to be found.
Determine the area under the standard normal curve that lies between (a) z = -2.55 and z = 2.55 (b) z = -1.67 and z = 0 (c) z = -3.03 and z = 1.98 Find the indicated areas. Be sure to draw a standard normal curve and shade the area that is to be found.
Determine the total area under the standard normal curve (a) to the left of z = -2 or to the right of z = 2 (b) to the left of z = -1.56 or to the right of z = 2.56 (c) to the left of z = -0.24 or to the right of z = 1.20 Find the indicated areas. Be sure to draw a standard normal curve and shade
Determine the total area under the standard normal curve (a) to the left of z = -2.94 or to the right of z = 2.94 (b) to the left of z = -1.68 or to the right of z = 3.05 (c) to the left of z = -0.88 or to the right of z = 1 Find the indicated areas. Be sure to draw a standard normal curve and
Find the value of za . z0.01
Find the value of za . z0.02
Find the value of za . z0.025
z0.15 Find the value of za .
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X > 35)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X > 65)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X ≤ 45)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X ≤ 58)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(40 < X < 65)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(56 < X < 68)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(55 ≤ X ≤ 70)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(40 ≤ X ≤ 49)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(38 < X ≤ 55)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(56 ≤ X < 66)
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X. The 9th percentile?
The 90th percentile Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X.
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X. The 81st percentile?
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X. The 38th percentile?
The mean incubation time of fertilized chicken eggs kept at 100.5°F in a still-air incubator is 21 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Source: University of Illinois Extension (a) What is the probability that a randomly
The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.(a) What is the probability that a randomly selected sixth-grade student reads less than 100 words per minute?(b) What is the probability that
The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and standard deviation 118 chips according to a study by cadets of the U.S. Air Force Academy. (a) What is the probability that a randomly selected
Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-throughs. Certainly, the faster the cars get through the drive-through, the more the opportunity for making money. QSR Magazine studied drive-through times for fast-food restaurants and found
The lengths of human pregnancies are approximately normally distributed, with mean µ = 266 days and standard deviation σ = 16 days. (a) What proportion of pregnancies lasts more than 270 days? (b) What proportion of pregnancies lasts less than 250 days? (c) What proportion of pregnancies lasts
Electric manufactures a decorative Crystal Clear 60-watt light bulb that it advertises will last 1500 hours. Suppose that the lifetimes of the light bulbs are approximately normally distributed, with a mean of 1550 hours and a standard deviation of 57 hours. (a) What proportion of the light bulbs
Steel rods are manufactured with a mean length of 25 centimeters (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed, with a standard deviation of 0.07 cm. (a) What proportion of rods has a length less than 24.9 cm? (b) Any
Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally distributed, with a standard deviation of 0.02 mm. (a) What proportion of ball bearings has a diameter more
In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points, and wins the game by 7
In games where a team is favored by more than 12 points, the margin of victory for the favored team relative to the spread is normally distributed with a mean of -1.0 point and a standard deviation of 10.9 points. (a) In games where a team is favored by more than 12 points, what is the probability
The mean incubation time of fertilized chicken eggs kept at 100.5°F in a still-air incubator is 21 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 17th percentile for incubation times of fertilized chicken
The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. (a) What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile? (b) A school psychologist wants to determine
The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cadets of the U.S. Air Force Academy. Source: Brad Warner and Jim Rutledge, Chance
Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-through. Certainly, the faster the cars get through the drive-through, the more the opportunity for making money. QSR Magazine studied drive-through times for fast-food restaurants, and found
The time required for Speedy Lube to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5 minutes. (a) Speedy Lube guarantees customers that the service will take no longer than 20 minutes. If it does
The following data represent the distribution of birth weights (in grams) for babies in which the pregnancy went full term (37 to 41 weeks).Birth Weight (g) ....Number of Live Births0–499 ........... 22500–999 .......... 2011000–1499 ........ 1,6451500–1999 ........ 9,3652000–2499
The ACT and SAT are two college entrance exams. The composite score on the ACT is approximately normally distributed with mean 21.1 and standard deviation 5.1. The composite score on the SAT is approximately normally distributed with mean 1026 with standard deviation 210. Suppose you scored 26 on
In a 1998 advertising campaign, Nabisco claimed that every 18-ounce bag of Chips Ahoy! Cookies contained at least 1000 chocolate chips. Brad Warner and Jim Rutledge tried to verify the claim. The following data represent the number of chips in an 18-ounce bag of Chips Ahoy! based on their study.(a)
A random sample of college students aged 18 to 24 years was obtained, and the number of hours of television watched in a typical week was recorded.(a) Use the following normal probability plot to determine if the data could have come from a normal distribution. (b) Determine the mean and standard
A random sample of O-rings was obtained, and the wall thickness (in inches) of each was recorded.Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.
A random sample of weekly work logs at an automobile repair station was obtained, and the average number of customers per day was recorded.Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.
A random sample of 20 undergraduate students receiving student loans was obtained, and the amount of their loans for the 2011€“2012 school year was recorded.Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.
A random sample of 25 years between 1890 and 2011 was obtained, and the amount of snowfall, in inches, for Memphis was recorded.Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.
Suppose X is a binomial random variable. To approximate P(X < 5), compute_______.
Suppose X is a binomial random variable. To approximate P(3 ≤ X ≤ 10), compute ____________.
The probability that at least 40 households have a gas stove A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the
The probability of no more than 20 people who want to see Roe v. Wade overturned A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we
The probability that exactly eight defective parts are in the shipment A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to
The probability that exactly 12 students pass the course A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the
The probability that the number of people with blood type O-negative is between 18 and 24, inclusive A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be
The probability that the number of tornadoes that occur in the month of May is between 30 and 40, inclusive A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be
The probability that more than 20 people want to see the marriage tax penalty abolished A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example,
The probability that fewer than 40 households have a pet A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the
The probability that more than 500 adult Americans support a bill proposing to extend daylight savings time A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be
The probability that fewer than 35 people support theprivatization of Social Security A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example,
n = 60, p = 0.4, x = 20Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so, approximate P(x) and compare the result to the exact probability.
n = 80, p = 0.15, x = 18Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so, approximate P(x) and compare the result to the exact probability.
n = 40, p = 0.25, x = 30 Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so, approximate P(x) and compare the result to the exact probability.
n = 100, p = 0.05, x = 50 Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so, approximate P(x) and compare the result to the exact probability.
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