Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In most applications, continuous random variables represent counted data, while discrete random variables represent measured data.
> You randomly select 18 adult male athletes and measure the resting heart rate of each. The sample mean heart rate is 64 beats per minute, with a sample standard deviation of 2.5 beats per minute. Assuming the heart rates are normally distributed, should
> Construct 90% and 95% confidence intervals for the population mean number of days the car model sits on the dealership’s lot in Example 3. Compare the widths of the confidence intervals.
> Construct 90% and 99% confidence intervals for the population mean temperature of coffee sold in Example 2.
> Find the critical value tc for a 90% confidence level when the sample size is 22.
> In Example 6, how many student-athletes must the researcher include in the sample to be 95% confident that the sample mean is within 0.75 hour of the population mean? Compare your answer with Example 6.
> Use the normal curves shown. Which normal curve has the greatest standard deviation? Explain your reasoning. B 80 90 100 110 120 130 140
> Construct a 90% confidence interval for the population mean age for the college students in Example 5 with the sample size increased to 30 students. Compare your answer with Example 5.
> Use the data in Example 1 and technology to construct 75%, 85%, and 90% confidence intervals for the mean number of hours spent on required athletic activities by all student-athletes in the conference. How does the width of the confidence interval chang
> Use the data in Try It Yourself 1 to construct a 95% confidence interval for the mean number of hours spent on required athletic activities by all student-athletes in the conference. Compare your result with the interval found in Example 3. From Try It
> Use the data in Try It Yourself 1 and a 95% confidence level to find the margin of error for the mean number of hours spent on required athletic activities by all student-athletes in the conference. Assume the population standard deviation is 2.3 hours.
> In Example 1, the researcher selects a second random sample of 30 student-athletes and records their numbers of hours spent on required athletic activities (see table at left). Use this sample to find another point estimate of the population mean m.
> The study in Example 5 found that 32.0% of all men in the United States ages 50 and older have arthritis. You randomly select 75 men in the United States who are at least 50 years old and ask them whether they have arthritis. What is the probability that
> In Example 4, what is the probability that at most 80 drivers will say yes, they have yelled at another driver?
> In a survey of adults in the United States, 29% said they have seen a person using a mobile device walk in front of a moving vehicle without looking. You randomly select 100 adults in the United States and ask them whether they have seen a person using a
> Use a continuity correction to convert each binomial probability to a normal distribution probability. 1. The probability of getting between 57 and 83 successes, inclusive 2. The probability of getting at most 54 successes
> A binomial experiment is listed. Determine whether you can use a normal distribution to approximate the distribution of x, the number of people who reply yes. If you can, find the mean and standard deviation. If you cannot, explain why. In a survey of a
> Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distri
> Which event(s) in Exercise 6 can be considered unusual? Explain your reasoning. From Exercise 6: Basketball player Dwight Howard makes a free throw shot about 56% of the time. Find the probability that a. the first free throw shot he makes is the fourt
> A consumer price analyst claims that prices for liquid crystal display (LCD) computer monitors are normally distributed, with a mean of $190 and a standard deviation of $48. What is the probability that a randomly selected LCD computer monitor costs less
> The average sales price of a single-family house in the United States is $235,500. You randomly select 12 single-family houses. What is the probability that the mean sales price is more than $225,000? Assume that the sales prices are normally distributed
> You randomly select 100 drivers ages 16 to 19 from Example 4. What is the probability that the mean distance traveled each day is between 19.4 and 22.5 miles? Use µ = 20.7 miles and σ = 6.5 miles.
> The diameters of fully grown white oak trees are normally distributed, with a mean of 3.5 feet and a standard deviation of 0.2 foot, as shown in the figure. Random samples of size 16 are drawn from this population, and the mean of each sample is determin
> Random samples of size 64 are drawn from the population in Example 2. Find the mean and standard deviation of the sampling distribution of sample means. Then sketch a graph of the sampling distribution and compare it with the sampling distribution in Exa
> List all possible samples of size n = 3, with replacement, from the population {1, 3, 5}. Calculate the mean of each sample. Find the mean, variance, and standard deviation of the sample means. Compare your results with the mean µ = 3, variance σ2 = 8 3,
> The lengths of time employees have worked at a corporation are normally distributed, with a mean of 11.2 years and a standard deviation of 2.1 years. In a company cutback, the lowest 10% in seniority are laid off. What is the maximum length of time an em
> A researcher tests the braking distances of several cars. The braking distance from 60 miles per hour to a complete stop on dry pavement is measured in feet. The braking distances of a sample of cars are normally distributed, with a mean of 129 feet and
> A veterinarian records the weights of dogs treated at a clinic. The weights are normally distributed, with a mean of 52 pounds and a standard deviation of 15 pounds. Find the weight x corresponding to each z-score. Interpret the results. 1. z = -2.33
> Find the z-score that corresponds to each percentile. 1. P10 2. P20 3. P99
> Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distri
> 1. Find the z-score that has 96.16% of the distribution’s area to its right. 2. Find the positive z-score for which 95% of the distribution’s area lies between -z and z.
> A U.S. adult who is at least 20 years old is selected at random. What is the probability that the person’s triglyceride level is between 100 and 150? Use technology to find the probability.
> What is the probability that the shopper in Example 2 will be in the supermarket between 31 and 58 minutes? When 200 shoppers enter the store, how many shoppers would you expect to be in the store between 31 and 58 minutes?
> The average speed of vehicles traveling on a stretch of highway is 67 miles per hour with a standard deviation of 3.5 miles per hour. A vehicle is selected at random. What is the probability that it is violating the speed limit of 70 miles per hour? Assu
> Find the area under the standard normal curve between z = -2.165 and z = -1.35.
> Find the area under the standard normal curve to the right of z = -2.16.
> Find the area under the standard normal curve to the left of z = 2.13.
> 1. Find the cumulative area that corresponds to a z-score of -2.19. 2. Find the cumulative area that corresponds to a z-score of 2.17.
> The scaled test scores for the New York State Grade 4 Common Core English Language Arts Test are normally distributed. The normal curve shown below represents this distribution. What is the mean test score? Estimate the standard deviation of this normal
> 1. Which normal curve has the greatest mean? 2. Which normal curve has the greatest standard deviation? B. 30 40 50 60 70
> Write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. P(54 < x < 64)
> Two thousand brown trout are introduced into a small lake. The lake has a volume of 20,000 cubic meters. Use a table to find the probability that three brown trout are found in any given cubic meter of the lake.
> What is the probability that more than four accidents will occur in any given month at the intersection?
> The study in Example 1 found that the smartphones made by a second manufacturer had a failure rate of 14%. Six smartphones made by this manufacturer are selected at random. Find the probability that the sixth smartphone is the first one to have a failure
> A recent study found that 28% of U.S. adults read an ebook in the last 12 months. You randomly select 4 adults and ask them whether they read an ebook in the last 12 months. Construct a probability distribution for the random variable x. Then graph the d
> About 5% of workers (ages 16 years and older) in the United States commute to their jobs by using public transportation (excluding taxicabs). You randomly select six workers. What is the probability that exactly two of them use public transportation to g
> The survey in Example 5 found that 27% of U.S. adults say that CNN is a major source of news for them. You randomly select five adults and ask them whether CNN is a major source of news for them. Find the probability that 1. exactly two of them respond
> A survey found that 52% of U.S. adults associate professional football with negative moral values. You randomly select 150 adults. What is the probability that exactly 65 adults associate professional football with negative moral values? Use technology t
> Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The mean of the random variable of a probability distribution describes how the outcomes vary.
> Determine whether the statement is true or false. If it is false, rewrite it as a true statement. For a random variable x, the word random indicates that the value of x is determined by chance.
> Write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. P(x < 60)
> What does the mean of a probability distribution represent?
> Is the expected value of the probability distribution of a random variable always one of the possible values of x? Explain.
> What is a discrete probability distribution? What are the two conditions that a discrete probability distribution must satisfy?
> What is a random variable? Give an example of a discrete random variable and a continuous random variable. Justify your answer.
> The random variable x is normally distributed with mean µ = 174 and standard deviation σ = 20. Find the indicated probability. P(x > 155)
> The random variable x is normally distributed with mean µ = 174 and standard deviation σ = 20. Find the indicated probability. P(x > 182)
> A control chart is shown. Each chart has horizontal lines drawn at the mean µ, at µ ± 2σ, and at µ ± 3σ. Determine whether the process shown is in control or out of
> A control chart is shown. Each chart has horizontal lines drawn at the mean µ, at µ ± 2σ, and at µ ± 3σ. Determine whether the process shown is in control or out of
> A control chart is shown. Each chart has horizontal lines drawn at the mean µ, at µ ± 2σ, and at µ ± 3σ. Determine whether the process shown is in control or out of
> A control chart is shown. Each chart has horizontal lines drawn at the mean µ, at µ ± 2σ, and at µ ± 3σ. Determine whether the process shown is in control or out of
> Write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. P(x > 14)
> Answer the questions about the specified normal distribution. Use the normal distribution in Exercise 16. a. What percent of the adult males have a red blood cell count less than 6 million cells per microliter? b. What percent of the adult males have a
> The random variable x is normally distributed with mean µ = 174 and standard deviation σ = 20. Find the indicated probability. P(x < 200)
> Answer the questions about the specified normal distribution. Use the normal distribution in Exercise 15. a. What percent of the new mothers had a pregnancy length of less than 290 days? b. What percent of the new mothers had a pregnancy length of betw
> Answer the questions about the specified normal distribution. Use the normal distribution in Exercise 14. a. What percent of the ACT composite scores are less than 19? b. Out of 1500 randomly selected ACT composite scores, about how many would you expe
> Answer the questions about the specified normal distribution. Use the normal distribution in Exercise 13. a. What percent of the SAT total scores are less than 1300? b. Out of 1000 randomly selected SAT total scores, about how many would you expect to
> A member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. Red Blood Cell Count in a Popu
> A member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. Pregnancy Length in a Populati
> A member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. ACT Composite Scores 28 <x<33
> A member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. SAT Total Scores 750 <x< 1000
> Find the indicated probabilities. If convenient, use technology to find the probabilities. The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standard deviation of 5 minutes. Find the
> Write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. P(x = 45)
> Find the indicated probabilities. If convenient, use technology to find the probabilities. The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $12. Find the probability that a randomly selected ut
> Find the indicated probabilities. If convenient, use technology to find the probabilities. In a recent year, the MCAT scores for the critical analysis and reasoning skills portion of the test were normally distributed, with a mean of 124.9 and a standard
> The random variable x is normally distributed with mean µ = 174 and standard deviation σ = 20. Find the indicated probability. P(x < 170)
> Why is it correct to say “a” normal distribution and “the” standard normal distribution?
> Describe how you can transform a nonstandard normal distribution to the standard normal distribution.
> What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution?
> For two values c and d, where a ≤ c ≤ d ≤ b, the probability that x lies between c and d is equal to the area under the curve between c and d, as shown below. So, the area of the red region equ
> Draw two normal curves that have different means but the same standard deviation. Describe the similarities and differences.
> Show that the probability density function of a uniform distribution satisfies the two conditions for a probability density function.
> Draw a normal curve with a mean of 450 and a standard deviation of 50. Describe how you constructed the curve and discuss its features.
> Write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. P(x ≤ 36)
> Draw a normal curve with a mean of 60 and a standard deviation of 12. Describe how you constructed the curve and discuss its features.
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < -1.22 or z > 1.32)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < -2.58 or z > 2.58)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(-1.54 < z < 1.54)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(-1.78 < z < 1.78)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(0 < z < 0.525)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(-0.89 < z < 0)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z > -1.85)
> Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences.
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z > 2.175)
> Write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. P(x ≥ 25)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < -0.18)
> Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < 1.16)
> Find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability. 1.68
> Find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability. -1 0 1
> Find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability. 1.28
> Find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability. -2.125
