Finding Probabilities In Exercise, find the

Problem 1E Find three real-life examples of a continuous variable. Which do you think may be normally distributed? Why?

Problem 2E In a normal distribution, which is greater, the mean or the median? Explain.

Problem 3E What is the total area under the normal curve?

Problem 4E What do the inflection points on a normal distribution represent? Where do they occur?

Problem 5E Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences.

Problem 6E Draw two normal curves that have different means but the same standard deviation. Describe the similarities and differences.

Problem 7E What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution?

Problem 8E Describe how you can transform a nonstandard normal distribution to the standard normal distribution.

Problem 9E Getting at the Concept Why is it correct to say “a” normal distribution and “the” standard normal distribution?

Problem 10E Getting at the Concept A z-score is 0. Which of these statements must be true? Explain your reasoning. (a) The mean is 0. ________________ (b) The corresponding x-value is 0. ________________ (c) The corresponding x-value is equal to the mean.

Problem 11E Graphical Analysis In Exercise, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Problem 12E Graphical Analysis In Exercise, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Problem 13E Graphical Analysis In Exercise, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Problem 14E Graphical Analysis In Exercise, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Problem 15E Graphical Analysis In Exercise, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Problem 19E Graphical Analysis In Exercise, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area.

Problem 20E Graphical Analysis In Exercise, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area.

Problem 21E Graphical Analysis In Exercise, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area.

Problem 22E Graphical Analysis In Exercise, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area.

Problem 23E Graphical Analysis In Exercise, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area

Problem 24E Graphical Analysis In Exercise, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area .

Problem 25E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = 0.08

Problem 26E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = -3.16

Problem 27E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = -2.575

Problem 28E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = 1.365

Problem 29E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = -0.65

Problem 30E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = 3.25

Problem 31E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = -0.355

Problem 32E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = 1.615

Problem 33E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = 0 and z = 2.86

Problem 34E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = -1.53 and z = 0

Problem 35E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = -1.96 and z = 1.96

Problem 36E Finding Area In Exercise, 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

Problem 37E Finding Area In Exercise, 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

Problem 39E Manufacturer Claims 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 miles. You test 16 tires and record the life spans shown below. 48,778 41,046 29,083 36,394 32,302 42,787 41,972 37,229 25,314 31,920 38,030 38,445 30,750 38,886 36,770 46,049 (a) Draw a frequency histogram to display these data. Use five classes. Do the life spans appear to be normally distributed? Explain. ________________ (b) Find the mean and standard deviation of your sample. ________________ (c) Compare the mean and standard deviation of your sample with those in the manufacturer’s claim. Discuss the differences.

Problem 40E Milk Consumption 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 30 people and record the weekly milk consumptions shown below. 40 45 54 41 43 31 47 30 33 37 48 57 52 45 38 65 25 39 53 51 58 52 40 46 44 48 61 47 49 57 (a) Draw a frequency histogram to display these data. Use seven classes. Do the consumptions appear to be normally distributed? Explain. ________________ (b) Find the mean and standard deviation of your sample. ________________ (c) Compare the mean and standard deviation of your sample with those of the previous study. Discuss the differences.

Problem 45E Graphical Analysis In Exercise, find the probability of z occurring in the indicated region of the standard normal distribution. If convenient, use technology to find the probability.

Problem 46E Graphical Analysis In Exercise, find the probability of z occurring in the indicated region of the standard normal distribution. If convenient, use technology to find the probability.

Problem 47E Graphical Analysis In Exercise, find the probability of z occurring in the indicated region of the standard normal distribution. If convenient, use technology to find the probability.

Problem 48E Graphical Analysis In Exercise, find the probability of z occurring in the indicated region of the standard normal distribution. If convenient, use technology to find the probability.

Problem 49E Graphical Analysis In Exercise, find the probability of z occurring in the indicated region of the standard normal distribution. If convenient, use technology to find the probability.

Problem 50E Graphical Analysis In Exercise, find the probability of z occurring in the indicated region of the standard normal distribution. If convenient, use technology to find the probability.

Problem 51E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < 1.45)

Problem 52E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < -0.18)

Problem 53E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z > 2.175)

Problem 54E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z > -1.85)

Problem 55E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(-0.89<z < 0)

Problem 56E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(0<z < 0.525)

Problem 57E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(-1.65<z < 1.65)

Problem 58E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(-1.54<z < 1.54)

Problem 59E Finding Probabilities In Exercise, 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)

Problem 60E Finding Probabilities In Exercise, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < -1.54 or z > 1.54)

Problem 61E Writing 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.

Problem 62E Writing 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.

Problem 38E Finding Area In Exercise, find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the left of z = -1.96 and to the right of z = 1.96