A continuous variable will be a measurable quantity such as height, weight, temperature, etc.
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]]>You work for a consumer watchdog publication and are testing the advertising claims of a lightbulb manufacturer. The manufacturer claims that the life span of the bulb is normally distributed, with a mean of 2000 hours and a standard deviation of250 hours. You test 20 lightbulbs and get the following life spans.
2210 | 2406 | 2267 | 1930 | 2005 | 2502 | 1106 | 2140 | 1949 | 1921 |
2217 | 2121 | 2004 | 1397 | 1659 | 1577 | 2840 | 1728 | 1209 | 1639 |
As the size of the sample increases, the mean of the distribution of sample means increase.
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A sampling distribution is only normal if the population is normal.
If the size of a sample is at least 30, you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.
The heights of fully grown sugar maple trees are normally distributed, with a mean of #m feet and a standard deviation of #sd feet. Random samples of size #n are drawn from the population and the mean of each sample is determined.
The mean price of digital cameras at an electronics store is $#m, with a standard deviation of $#sd. Random samples of size #n are drawn from this population and the mean of each sample is determined
The per capita consumption of red meat by people in the United states in a recent year is was normally distributed, with a mean of #m pounds and a standard deviation of #sd pounds. Random samples of size #n are drawn from this population and the mean of each sample is determined.
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The population mean annual salary for plumbers is $46,700. A random sample of 42 plumbers is drawn from this population. What is the probability (to three significant figures) that the mean salary of the sample is less than $44,000? Assume «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math»$5600.
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During a certain week the mean price of gasoline in the New England region was $2.818 per gallon. A random sample of 32 gass stations is drawn from this population. What is the probability that the mean price for the sample was between $2.768 and $2.918 that week? Assume «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math»$0.045.
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The mean height of a woman in the United States (ages 20-29) is 64.1 inches. A random sample of 60 women in this age group is selected. What is the probability that the mean height for the sample is greater than 66 inches? Assume «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math»2.71.
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]]>A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces. Does the machine need to be reset? Explain your reasoning.
]]>Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 8 feet (96 inches) with a standard deviation of 0.5 inch. Assume the lengths are normally distributed. You randomly select 40 boards and find that the mean length is 96.25 inches.
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]]>A survey was conducted to measure the height of U.S. men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.6 inches and a standard deviation of 3.0 inches. A study participant is randomly selected.
The lengths of Atlantic croaker fish are normally distributed, with a mean of 10 inches and a standard deviation of 2 inches. An Atlantic croaker fish is randomly selected.
In a recent year, the ACT scores for high school students with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 24.2 and a standard deviation of 4.3. A student with a 3.50 to 4.00 grade point average who took the ACT during this time is randomly selected.
The weights of adult male beagles are normally distributed, with a mean of 25 pounds and a standard deviation of three pounds. A beagle is randomly selected.
A survey was conducted to measure the number of hours per week adults in the United states spend on home computers. In the survey, the number of hours were normally distributed, with a mean of 7 hours and a standard deviation of 1 hour. A survey participant is randomly selected.
The monthly utility bills in a city are normally distributed with a mean of $100 and a standard deviation of $12. A utility bill is randomly selected.
The time per week a student uses a lab computer is normally distributed, with a mean of 6.2 hours and a standard deviation of 0.9 hour. A student is randomly selected.
The time per workout an athlete uses a stairclimber is normally distributed, with a mean of 20 minutes and a standard deviation of 5 minutes. An athlete is randomly selected.
The normal distribution of SAT critical reading scores for a certain year has a mean of 503 and a standard deviation of 113.
The normal distribution of SAT math scores for a certain year has a mean of 518 and a standard deviation of 115.
The normal distribution of U.S. woman's total cholesterol levels in the age group of 20-34 has a mean of 186 milligrams per deciliter and a standard deviation of of 35.8 milligrams per deciliter.
The normal distribution of U.S. woman's total cholesterol levels in the age group of 55-64 has a mean of 219 milligrams per deciliter and a standard deviation of of 41.6 milligrams per deciliter.
The normal distribution for Atlantic croaker fish lengths has a mean of 10 inches and a standard deviation of 2 inches.
The normal distribution of the weight of adult male beagles has a mean of 25 pounds and a standard deviation of 3 pounds.
The normal distribution of home computer use in U.S adults has a mean of 7 hours and a standard deviation of 1 hour.
The normal distribution of monthly utility bills in a city has a mean of $100 and a standard deviation of $12.
The life span of a battery is normally distributed, with a mean of 2000 hours and a standard deviation of 30 hours.
Assume the mean annual consumption of peanuts is normally distributed, with a mean of 5.9 pounds per person and a standard deviation of 1.8 pounds per person.
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In a survey of women in the United States (ages 20-29), the mean height was 64.1 inches with a standard deviation of 2.71 inches.
In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches.
The annual per capita utilization of apples (in pounds) in the Uniteed States can be approximated by a normal distribution, as shown in the graph.
The annual per capita utilization of oranges (in pounds) in the United States can be approximated by a normal distribution, as shown in the graph.
The time spent (in days) waiting for a heart transplant in Ohio and Michigan for patients with type A+ blood can be approximated by a normal distribution, as shown in the graph.
The annual per capita consumption of ice cream (in pounds) in the United States can be approximated by a normal distribution, as shown in the graph.
The weights of the contents of a cereal box are normally distributed with a mean weight of 20 ounces and a standard deviation of 0.07 ounce. Boxes in the lower 5% do not meet the minimum weight requirements and must be repackaged. What is the minimum weight requirement for the cereal box?
Answer:{#1} ounces
]]>The weights of bags of baby carrots are normally distributed with a mean of 32 ounces and a standard deviation of 0.36 ounce. Bags in the upper 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be repackaged?
Answer:{#1} ounces
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