Find the z-score such that the area under the standard normal curve to its left is 0.1.
> 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 and standa
> Explain why P(X ≤220) should be reported as > 0.9999 if X is a normal random variable with mean 100 and standard deviation 15.
> Explain why P(X < 30) should be reported as
> Give three interpretations for the area under a normal curve.
> The file 7_2_53 represents distance (in feet) of all home runs hit during the 2018 Major League baseball season. It is available at www.pearsonhighered.com/sullivanstats. (a) Draw a relative frequency histogram of the home run distances using a lower cla
> The following data represent the distribution of birth weights (in grams) for babies in which the pregnancy went full term (37–41 weeks). (a) Construct a relative frequency distribution for birth weight. (b) Draw a relative frequency histogram for birth
> 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 wil
> Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-thru. Certainly, the faster the cars get through the drive-thru, the more the opportunity for making money. QSR Magazine studied drive-thru times for fa
> 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. S
> In an effort to identify whether an advertising campaign has been effective, a marketing firm conducts a nationwide poll by randomly selecting individuals from a list of known users of the product.
> 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? (
> 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
> See Problem 45. 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. Source: Justin Wolfers,
> 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 fa
> 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 prop
> 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
> Using a technique referred to as the “Hi-Opt I System” in the casino game blackjack, a player can expect to earn $1.65 per shoe of cards with a standard deviation of $48.93 with a $1 bet per hand. The earnings are approximately normally distributed. This
> The lengths of human pregnancies are approximately normally distributed, with mean = 266 days and standard deviation = 16 days. (a) What proportion of pregnancies lasts more than 270 days? (b) What proportion of pregnancies lasts less than 250 days?
> The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and an individua
> 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. Source:
> A member of Congress wishes to determine her constituency’s opinion regarding estate taxes. She divides her constituency into three income classes: low-income households, middle-income households, and upper-income households. She then takes a simple rand
> Grams of carbohydrates in a doughnut
> 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) Draw a normal model that describes the reading speed of sixth-grade students. (b) Find and i
> 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
> The 38th percentile
> The 81st percentile
> The 90th percentile
> The 9th percentile
> P(56 ≤ X < 66)
> P(38 < X ≤ 55)
> P(40 ≤ X ≤ 49)
> P(55 ≤ X ≤ 70)
> To determine customer opinion of its boarding policy, Southwest Airlines randomly selects 60 flights during a certain week and surveys all passengers on the flights.
> P(56 < X < 68)
> P(40 < X < 65)
> P(X ≤ 58)
> P(X ≤ 45)
> P(X > 65)
> P(X > 35)
> z0.15
> z0.025
> z0.02
> z0.01
> To determine the prevalence of human growth hormone (HGH) use among high school varsity baseball players, the State Athletic Commission randomly selects 50 high schools. All members of the selected high schools’ varsity baseball teams are tested for HGH.
> Find the z-scores that separate the middle 94% of the distribution from the area in the tails of the standard normal distribution.
> Find z-scores that separate the middle 99% of the distribution from the area in the tails of the standard normal distribution.
> Find the z-score such that the area under the standard normal curve to its right is 0.35.
> Find the z-score such that the area under the standard normal curve to its right is 0.25.
> Find the z-score such that the area under the standard normal curve to its left is 0.2.
> 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 = 1.23
> 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
> 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
> 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
> To estimate the percentage of defects in a recent manufacturing batch, a quality-control manager at Intel selects every 8th chip that comes off the assembly line starting with the 3rd until she obtains a sample of 140 chips.
> 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
> 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
> 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
> The area under a normal curve can be interpreted as a_____ or_____ .
> What are the properties of the normal density curve?
> A_____ is an equation, table, or graph used to describe reality.
> What are the two properties that a probability density function must satisfy?
> Researchers conducted a prospective cohort study in which male patients who had an out-of-hospital cardiac arrest were submitted to therapeutic hypothermia (intravenous infusion of cold saline followed by surface cooling with the goal of maintaining body
> The following data represent the heights (in inches) of 80 randomly selected five-year-old females. (a) Use statistical software to construct a relative frequency histogram. Comment on the shape of the distribution. Draw a normal density curve on the rel
> 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 finder and hit 75 golf balls with his pitching wedge and measured the distance each ball traveled (in yards). H
> When obtaining a stratified sample, the number of individuals included within each stratum must be equal.
> Elena conducts an experiment in which she fills up the gas tank on her Toyota Camry 40 times and records the miles per gallon for each fill-up. A histogram of the miles per gallon (mpg) indicates that a normal distribution with a mean of 24.6 mpg and a s
> The lengths of human pregnancies are normally distributed with = 266 days and = 16 days. (a) The figure represents the normal curve with = 266 days and = 16 days. The area to the right of x = 280 days is 0.1908. Provide two interpretations of th
> The heights of 10-year-old males are normally distributed with mean = 55.9 inches and = 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
> The birth weights of full-term babies are normally distributed with mean = 3400 grams and = 505 grams. Source: Based on data obtained from the National Vital Statistics Report, Vol. 48, No. 3. (a) Draw a normal curve with the parameters labeled. (b)
> The length of a 10-year- old female’s upper leg is approximately normally distributed with mean = 33.8 cm and standard deviation = 2.1 cm. Source: Vital and Health Statistics, U.S. Department of Health and Human Services. (a) Draw a normal curve with
> The length of a 4-year-old male’s upper arm is approximately normally distributed with mean = 21.8 cm and standard deviation = 2.0 cm. Source: Vital and Health Statistics, U.S. Department of Health and Human Services. (a) Draw a normal curve with the
> = 50 and = 5
> = 30 and = 10
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>
> Inferences based on voluntary response samples are generally not reliable.
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>
> One graph in the figure below represents a normal distribution with mean = 8 and standard deviation = 2. The other graph represents a normal distribution with mean = 14 and standard deviation = 2. Determine which graph is which and explain how yo
> One graph in the figure below represents a normal distribution with mean = 10 and standard deviation = 3. The other graph represents a normal distribution with mean m = 10 and standard deviation = 2. Determine which graph is which and explain how
> The relative frequency histogram on the following page represents the incubation times of a random sample of Rhode Island Red hens’ eggs.
> The relative frequency histogram represents the length of phone calls on my wife’s cell phone during the month of September.
> The relative frequency histogram represents the waiting times (in minutes) to ride the American Eagle Roller Coaster for 2000 randomly selected people on a Saturday afternoon in the summer.
> The relative frequency histogram represents the birth weights (in grams) of babies whose term was 36 weeks.
> The reaction time X (in minutes) of a certain chemical process follows a uniform probability distribution with / (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 prob
> 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 probabilit
> When conducting a cluster sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.
> Find the probability that your friend is no more than 5 minutes late.
> Find the probability that your friend is at least 20 minutes late.
> (a) Find the probability that your friend is between 15 and 25 minutes late. (b) It is 10 A.M. There is a 90% probability your friend will arrive within the next ___ minutes.
> (a) Find the probability that your friend is between 5 and 10 minutes late. (b) It is 10 A.M. There is a 40% probability your friend will arrive within the next ___ minutes.
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> A simple random sample is always preferred because it obtains the same information as other sampling plans but requires a smaller sample size.
> (a) A binomial experiment is performed a fixed number of times. Each repetition of the experiment is called a_____ . (b) For each repetition of a binomial experiment, there are two mutually exclusive outcomes:____ or_____ .
> State the criteria for a binomial probability experiment.
