6. Normal Distribution and Continuous Random Variables

The mean gestational length of a sample of 208 horses is 343.7 days, with a standard deviation of 10.4 days. The data set has a bell-shaped distribution.

b. Determine whether a gestational length of 318.4 days is unusual.

The per capita disposable income for residents of a U.S. city in a recent year is normally distributed, with a mean of about \$44,000 and a standard deviation of about \$2450. Use this information in Exercises 7–10.

Out of 800 residents, about how many would you expect to have a disposable income of between \$40,000 and \$42,000?

Life Spans of Tires A brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.

b. The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.

Life Spans of Fruit Flies The life spans of a species of fruit fly have a bell-shaped distribution, with a mean of 33 days and a standard deviation of 4 days.

b. The life spans of three randomly selected fruit flies are 29 days, 41 days, and 25 days. Using the Empirical Rule, find the percentile that corresponds to each life span.

Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(z < - 1.11)

Finding a z-Score In Exercises 1–16, use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.

P33

Finding a z-Score In Exercises 1–16, use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.

P1.5

Finding a z-Score In Exercises 1–16, use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.

P91

Graphical Analysis In Exercises 17–22, find the indicated z-score(s) shown in the graph.

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Graphical Analysis In Exercises 17–22, find the indicated z-score(s) shown in the graph.

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Finding a z-Score Given an Area In Exercises 23–30, find the indicated z-score.

Find the z-score that has 78.5% of the distribution’s area to its left.

Finding a z-Score Given an Area In Exercises 23–30, find the indicated z-score.

Find the z-score that has 2.275% of the distribution’s area to its left.

Finding a z-Score Given an Area In Exercises 23–30, find the indicated z-score.

Find the positive z-score for which 12% of the distribution’s area lies between and z.

In Exercises 33 and 34, find the indicated probabilities. If convenient, use technology to find the probabilities.

The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean of 9.1 picomoles per liter and a standard deviation of 3.5 picomoles per liter. Find the probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is

a. between 5.1 and 15.7 picomoles per liter.

Find the positive z-score for which 94% of the distribution’s area lies between -z and z.