We assume the lunch prices we observe are drawn from a normal distribution with true mean 
and standard deviation 0.68 in dollars.
We average 
samples to get 
.
The standard deviation of the average (an experiment where we collect 45 samples and average them) is the square root of n times smaller than than the standard deviation of the individual samples. We'll write
Our goal is to come up with a confidence interval (a,b) that we can be 90% sure contains .
Our interval takes the form of 
as is our best guess at the middle of the interval. We have to find the z that gives us 90% of the area of the bell in the "middle".
Since we're given the standard deviation of the true distribution we don't need a t distribution or anything like that. n=45 is big enough (more than 30 or so) that we can substitute the normal distribution for the t distribution anyway.
Usually the questioner is nice enough to ask for a 95% confidence interval, which by the 68-95-99.7 rule is plus or minus two sigma. Here it's a bit less; we have to look it up.
With the right table or computer we find z that corresponds to a probability p=.90 the integral of the unit normal from -z to z. Unfortunately these tables come in various flavors and we have to convert the probability to suit. Sometimes that's a one sided probability from zero to z. That would be an area aka probability of 0.45 from 0 to z (the "body") or a probability of 0.05 from z to infinity (the "tail"). Often the table is the integral of the bell from -infinity to positive z, so we'd have to find p=0.95 in that table. We know that the answer would be z=2 if our original p had been 95% so we expect a number a bit less than 2, a smaller number of standard deviations to include a bit less of the probability.
We find z=1.65 in the typical table has p=.95 from -infinity to z. So our 90% confidence interval is
in other words a margin of error of
dollars
That's around plus or minus 17 cents.
<span><span>SPOTLIGHT DEMYSTIFIED QUIZZES GALLERIES LISTS ON THIS DAY BIOGRAPHIES</span>SEARCH BRITANNICAWhat are you looking for?SearchBROWSE POPULAR TOPICS:<span>Pearl Harbor attack American Revolution Reign of Terror Photosynthesis Las Posadas</span></span><span>You have reached Britannica's public website.<span>For ad-free access to your Britannica School or Library account CLICK HERE</span></span><span>Chemical compound<span>WRITTEN BY: </span><span>Melvyn C. UsselmanRichard O.C. NormanSteven S. ZumdahlCarl R. Noller</span>See Article History<span><span>Chemical compound, any substance composed of identical moleculesconsisting of atoms of two or more chemical elements.<span><span>Methane, in which four hydrogen atoms are bound to a single carbon atom, is an example of a basic chemical compound. The structures of chemical compounds are influenced by complex factors, such as bond angles and bond length.Encyclopædia Britannica, Inc.</span></span>All the matter in the universe is composed of the atoms of more than 100 different chemical elements, which are found both in pure form and combined in chemical compounds. A sample of any given pure element is composed only of the atoms characteristic of that element, and the atoms of each element are unique. For example, the atoms that constitute carbon are different from those that make up iron, which are in turn different from those of gold. Every element is designated by a unique symbol consisting of one, two, or three letters arising from either the current element name or its original (often Latin) name. For example, the symbols for carbon, hydrogen, and oxygen are simply C, H, and O, respectively. The symbol for iron is Fe, from its original Latin name ferrum. The fundamental principle of the science of chemistry is that the atoms of different elements can combine with one another to form chemical compounds. Methane, for example, which is formed from the elements carbon and hydrogen in the ratio four hydrogen atoms for each carbon atom, is known to contain distinct CH4 molecules. The formula of a compound—such as CH4—indicates the types of atoms present, with subscripts representing the relative numbers of atoms (although the numeral 1 is never written).<span /></span></span><span><span>
</span></span></span>
Answer:
5.46π cm³
Step-by-step explanation:
Volume of sphere= 4/3πr³
= 4/3×π×(1.6)³ cm³
=5.46π cm³
hope this helped you!
Answer:
Cynthia = 12 guavas
Bessy = 36 guavas
Aicel = 72 guavas
Step-by-step explanation:
Total guavas = 120
Let
Cynthia = x
Bessy = 3x
Aicel = 2(3x)
= 6x
x + 3x + 6x = 120
10x = 120
x = 120/10
x = 12
Cynthia = x
= 12 guavas
Bessy = 3x
= 3(12)
= 36 guavas
Aicel = 6x
= 6 × 12
= 72 guavas
Total = 74 + 36 + 12
= 120 guavas
