The random variable x is normally distributed with mean µ = 174 and standard deviation σ = 20. Find the indicated probability. P(x < 170)
> 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.
> 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.
> 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
> 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
> Find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability. -0.625 0
> Find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability. 1.96
> a. Find the z-score that corresponds to each value and b. Determine whether any of the values are unusual. The test scores for the Law School Admission Test (LSAT) are normally distributed. In a recent year, the mean test score was 155.69 and the standa
> What do the inflection points on a normal distribution represent? Where do they occur?
> A binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of U.S. likely voters found that 11% thin
> a. Find the z-score that corresponds to each value and b. Determine whether any of the values are unusual. The test scores for the verbal reasoning and the quantitative reasoning sections of the Graduate Record Examination (GRE) are normally distributed
> You are performing a study about weekly per capita milk consumption. A previous study found weekly per capita milk consumption to be normally distributed, with a mean of 48.7 fluid ounces and a standard deviation of 8.6 fluid ounces. You randomly sample
> You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 4000 mi
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = -1.44 and to the right of z = 2.21
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = -1.28 and to the right of z = 1.28
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = -2.33 and z = 2.33
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = -1.55 and z = 1.55
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = -1.53 and z = 0
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = 0 and z = 2.86
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = 1.485
> A binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of U.S. adults found that 75% support lab
> What is the total area under the normal curve?
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = -0.355
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = 3.25
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = -0.65
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = 1.365
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = -2.575
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = -3.16
> Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = 0.17
> Find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area. -225
> Find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area. -0.7 1.2
