Questions and Answers of Statistics Informed Decisions Using Data

The probability that less than 57 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.
The probability that there are exactly 15 defective parts in a shipment.A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal
The probability that at most 39 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.
The probability that more than 350 Americans support the bill proposing to extend daylight savings time.A discrete random variable is given. Assume the probability of the random variable will be
The probability that the number of people with blood type O-negative is between 18 and 27.A discrete random variable is given. Assume the probability of the random variable will be approximated using
n = 40, p = 0.3, x = 20 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,
A certain flight arrives on time 87 percent of the time. Suppose 149 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that(a) exactly 127
In the Healthy Handwashing Survey conducted by Bradley Corporation, it was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose you survey a
According to a study, 73% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home.) Suppose that a survey is administered
Find the value of z0.20 .
Find the value of z0.04.
An intelligence quotient, or IQ, is a measurement of intelligence derived from a standardized test, such as the Stanford Binet IQ test. Scores on this test are approximately normally distributed with
Repeat the problem in Example 1 with a sample of size n = 25.Approach Use the approach presented in Example 1, but let n = 25 instead of n = 9.Data from Example 1 An intelligence quotient, or IQ, is
The IQ, X, of humans is approximately normally distributed with mean μ = 100 and standard deviation σ = 15. Compute the probability that a simple random sample of size n = 10 results in a sample
The data in Table 1 represent the probability distribution of the number of people living in households in the United States. Figure 6 shows a graph of the probability distribution. From the data in
The mean weight gain during pregnancy is 30 pounds, with a standard deviation of 12.9 pounds. Weight gain during pregnancy is skewed right. An obstetrician obtains a random sample of 35 low-income
A simple random sample of size n = 55 is obtained from a population with μ = 82 and σ = 2. Does the population need to be normally distributed for the sampling distribution of x to be approximately
μ = 78, σ = 14, n = 49 Determine μx̅ and σx̅ from the given parameters of the population and the sample size.
μ = 80, σ = 36, n = 81 Determine μx̅ and σx̅ from the given parameters of the population and the sample size.
μ = 63, σ = 5, n = 21 Determine μx̅ and σx̅ from the given parameters of the population and the sample size.
μ = 42, σ = 14, n = 20 Determine μx̅ and σx̅ from the given parameters of the population and the sample size.
A simple random sample of size n = 64 is obtained from a population with μ = 83 and σ = 32.(a) Describe the sampling distribution of x̅.(b) What is P(x̅ > 88.6)?(c) What is P(x̅ ≤ 74)?(d) What
A simple random sample of size n = 12 is obtained from a population with μ = 69 and σ = 15.(a) What must be true regarding the distribution of the population in order to use the normal model to
A simple random sample of size n = 12 is obtained from a population with μ = 63 and σ = 19.(a) What must be true regarding the distribution of the population in order to use the normal model to
The reading speed of second-grade students in a large city is approximately normal, with a mean of 92 words per minute (wpm) and a standard deviation of 10 wpm.(a) What is the probability a randomly
Suppose a geyser has a mean time between eruptions of 74 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 26 minutes, answer the following
A very good poker player is expected to earn $$1$ per hand in $$100$/$$200$ Texas Hold’em. The standard deviation is approximately $$32$.(a) What is the probability a very good poker player
The Harris Poll conducted a survey of 1200 adult Americans who vacation during the summer and asked whether the individuals plan to work while on summer vacation. Of those surveyed, 552 indicated
Based on a study conducted by the Gallup organization, 76% of Americans believe that the state of moral values in the United States is getting worse. Describe the sampling distribution of the sample
Based on a study conducted by the Gallup organization, 76% of Americans believe that the state of moral values in the United States is getting worse. Suppose we obtain a simple random sample of n =
According to the National Center for Health Statistics, 15% of all Americans have hearing trouble.(a) In a random sample of 120 Americans, what is the probability at most 12% have hearing trouble?(b)
In a town of 500 households, 220 have a dog. The population proportion of dog owners in this town (expressed as a decimal) is p = ______ .
True or False: The mean of the sampling distribution of p̂ is p.
n = 200, p = 0.4. Assume the size of the population is 10,000.Describe the sampling distribution of p̂.
n = 800, p = 0.4. Assume the size of the population is 20,000.Describe the sampling distribution of p̂.
n = 1000, p = 0.706. Assume the size of the population is 25,000.Describe the sampling distribution of p̂.
n = 800, p = 0.476. Assume the size of the population is 20,000.Describe the sampling distribution of p̂.
A simple random sample of size n = 150 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.6.(a) Describe the sampling
A simple random sample of size n = 1000 is obtained from a population whose size is N = 1,500,000 and whose population proportion with a specified characteristic is p = 0.44. Complete parts (a)
According to a study conducted by an organization, the proportion of Americans who were afraid to fly in 2006 was 0.10.A random sample of 1,200 Americans results in 132 indicating that they are
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 25 adult Americans and asks them whether or not they support the proposed changes. To say
Finite Population Correction Factor In this section, we assumed that the sample size was less than 5% of the size of the population. When sampling without replacement from a finite population in
Refer to the situation in Example 1.(a) What is the probability your friend will be between 10 and 20 minutes late?(b) It is 10 a.m. There is a 20% probability your friend will arrive within the next
The relative frequency distribution given in Table 1 represents the heights of a pediatrician’s three-year-old female patients. The raw data indicate that the mean height of the patients is μ =
The serum total cholesterol for males 20–29 years old is approximately normally distributed with mean μ = 180 and σ = 36.2, based on data obtained from the National Health and Nutrition
One graph in the figure below 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
The graph of a normal curve is given. Use the graph to identify the values of μ and σ. -7-4-1 2 5 8 11 X
The graph of a normal curve is given. Use the graph to identify the values of μ and σ. -1 1 3 5 7 9 11 X
The graph of a normal curve is given. Use the graph to identify the values of μ and σ. 55 70 85 100 115 130 145 X
The graph of a normal curve is given. Use the graph to identify the values of μ and σ. 230 330 430 530 630 730 830 X
A pediatrician obtains the heights of her three-year-old female patients. The heights are approximately normally distributed, with mean 38.72 inches and standard deviation 3.17 inches. Use the normal
For the pediatrician presented in Example 1, find the probability that a randomly selected three-year-old girl is between 35 and 40 inches tall, inclusive. That is, find P(35 ≤ X ≤ 40).By-Hand
The heights of a pediatrician’s three-year-old females are approximately normally distributed, with mean 38.72 inches and standard deviation 3.17 inches. Find the height of a three-year-old female
The scores earned on the mathematics portion of the SAT, a college entrance exam, are approximately normally distributed with mean 516 and standard deviation 116. What scores separate the middle 90%
Find the value of z0.10.Approach We wish to find the z-value such that the area under the standard normal curve to the right of the z-value is 0.10.
z0.01 Find the value of zα.
z0.02 Find the value of zα.
z0.025 Find the value of zα.
z0.15 Find the value of zα.
The data in Table 4 represent the finishing time (in seconds) for six randomly selected races of a greyhound named Barbies Bomber in the 5/16 -mile race at Greyhound Park in Dubuque, Iowa. Is there
Draw a normal probability plot of the data in Table 4 using technology. Is there evidence to support the belief that the variable “finishing time” is normally distributed?Approach We will use
According to the American Red Cross, 7% of people in the United States have blood type O-negative. What is the probability that, in a simple random sample of 500 people in the United States, fewer
According to the Gallup Organization, 65% of adult Americans are in favor of the death penalty for individuals convicted of murder. Erica selects a random sample of 1000 adult Americans in Will
N = 230, n = 15, k = 200 Compute the mean and standard deviation of the hypergeometric random variable X.
One study showed that in a certain year, airline fatalities occur at the rate of 0.011 deaths per 100 million miles. Find the probability that, during the next 100 million miles of flight, there will
N = 60, n = 8, k = 25 Compute the mean and standard deviation of the hypergeometric random variable X.
Assuming μ = 5, compute(a) P(5)(b) P(X < 5)(c) P(X ≥ 5)(d) P(5 ≤ X ≤ 7)The random variable X follows a Poisson process with the given mean.
(a) Graph the binomial probability distribution with n = 10 and p = 0.2. Comment on the shape of the distribution.(b) Graph the binomial probability distribution with n = 10 and p = 0.5. Comment on
According to CTIA, 41% of all U.S. households are wireless-only households. In a simple random sample of 300 households, determine the mean and standard deviation number of wireless-only
In a neighborhood of 95 homes, 35 have pets. Suppose that 12 homes are selected at random. The random variable X represents the number of homes in the sample that have pets.Verify that the following
Determine whether the probability experiment represents a binomial experiment. If not, explain why.(a) An urn contains 20 colored golf balls: 8 white, 6 red, 4 blue, and 2 yellow. A child is allowed
The flaws in a piece of timber occur at the rate of 0.05 per linear foot. The random variable X is the number of flaws in the next 14 linear feet of timber.State the values of λ and t for each
What criteria must be satisfied for a random variable X to be a hypergeometric random variable?
According to the American Red Cross, 7% of people in the United States have blood type O-negative. A simple random sample of size 4 is obtained, and the number of people X with blood type O-negative
Explain the similarities and differences between the hypergeometric probability distribution and the binomial probability distribution.
Determine which of the following probability experiments qualify as binomial experiments. For those that are binomial experiments, identify the number of trials, probability of success, probability
A McDonald’s manager knows that cars arrive at the drive-through at the average rate of two cars per minute between the hours of 12 noon and 1:00 p.m.Determine and interpret the probability of the
Suppose that a researcher goes to a small college with 200 faculty, 12 of whom have blood type O-negative. She obtains a simple random sample of n = 20 of the faculty and finds that three of the
A biologist performs an experiment in which 2000 Asian beetles are allowed to roam in an enclosed area of 1000 square feet. The area is divided into 200 subsections of 5 square feet each.(a) If the
Suppose a researcher goes to a small college with 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample of n = 20 of the faculty. Let the random variable X represent
At the Wimbledon Tennis Championship, to win a match in men’s singles a player must win the best of five sets. The following data represent the number of sets played, X, in the men’s singles
According to CTIA, 41% of all U.S. households are wireless-only households(no landline). In a random sample of 20 households, what is the probability that(a) exactly 5 are wireless-only?(b) fewer
According to the Gallup Organization, 65% of adult Americans are in favor of the death penalty for individuals convicted of murder. In a random sample of 15 adult Americans, what is the probability
Suppose that a machine shop orders 500 bolts from a supplier. To determine whether to accept the shipment of bolts, the manager of the facility randomly selects 12 bolts. If none of the 12 randomly
The hits to a Web site occur at the rate of 8 per minute between 7:00 p.m. and 8:00 p.m. The random variable X is the number of hits to the Web site between 7:15 p.m. and 7:38 p.m.State the values of
When listing the possible values of the hypergeometric random variable X, it must be the case that x is less than or equal to the smaller of n or k. Why?
In your own words, explain the logic behind Formula (1).Formula 1 P(x) = (C) (N-KCn-x) NCn (1)
Suppose that a machine shop orders 500 bolts from a supplier. To determine whether to accept the shipment of bolts, the manager of the facility randomly selects 12 bolts. If none of the 12 randomly
According to the Gallup Organization, 65% of adult Americans are in favor of the death penalty for individuals convicted of murder. In a random sample of 15 adult Americans, what is the probability
Suppose that a researcher goes to a small college with 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample of n = 20 of the faculty. Determine the mean and
In Michigan’s Winfall Lottery, a player must choose six numbers between 1 and 49, inclusive. Six balls numbered between 1 and 49 are then randomly selected from an urn. The random variable X
A manufacturer received an order of 250 computer chips. Unfortunately, 12 of the chips are defective. To test the shipment, the quality-control engineer randomly selects 20 chips from the box of 250
According to CTIA, 41% of all U.S. households are wireless-only. In a simple random sample of 300 households, 143 were wireless-only. Is this result unusual?Approach Because np(1 - p) = 300(0.41)(1 -
Assuming μ = 4, compute the following.(a) P(4)(b) P(X < 4)(c) P(X ≥ 4)(d) P(3 ≤ X ≤ 5)The random variable X follows a Poisson process with the given mean.
A baseball team has 25 players, seven of whom bat lefthanded. Suppose that the manager of this team is frustrated with the way the team is playing, so he decides to randomly select nine players to
Assuming λ = 0.11 and t = 10, compute the following.(a) P(4)(b) P(X < 4)(c) P(X ≥ 4)(d) P(3 ≤ X ≤ 7)(e) μX and σXThe random variable X follows a Poisson process with the given value of λ
N = 150, n = 20, k = 30, x = 5 A hypergeometric probability experiment is conducted with the given parameters. Compute the probability of obtaining x successes.
The random variable X follows a Poisson process with λ = 0.05 and t = 8. Find each of the following:(a) P(3)(b) P(X < 3)(c) P(X ≥ 3)(d) P(3 ≤ X ≤ 5)(e) What are μX and σX?
Assuming λ = 0.08 and t = 15, compute the following.(a) P(5)(b) P(X < 5)(c) P(X ≥ 5)(d) P(5 ≤ X ≤ 7)(e) μX and σXThe random variable X follows a Poisson process with the given value of λ
N = 60, n = 8, k = 25, x = 3 A hypergeometric probability experiment is conducted with the given parameters. Compute the probability of obtaining x successes.

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