As the size of the sample increases, the mean of the distribution of sample means increase.
]]>As the size of the sample increases, the standard deviation of the distribution of the sample means increases.
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»$5600.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mover»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo»§lt;«/mo»«mo»$«/mo»«mn»44«/mn»«mo»,«/mo»«mn»000«/mn»«/mrow»«/mfenced»«mo»=«/mo»«/math» {#1}
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»$0.045.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mo»$«/mo»«mn»2«/mn»«mo».«/mo»«mn»768«/mn»«mo»§lt;«/mo»«mover»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo»§lt;«/mo»«mn»2«/mn»«mo».«/mo»«mn»918«/mn»«/mrow»«/mfenced»«mo»=«/mo»«/math» {#1}
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.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»(«/mo»«mover»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo»§#62;«/mo»«mn»66«/mn»«mo»§#160;«/mo»«mtext»inches)«/mtext»«mo»=«/mo»«/math»{#1}
]]>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.