A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 49 years old. Suppose that this measure is valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.(a) According to Chebyshev's theorem, at least 56 75 84 89 of the home buyers' ages lie within 2.5 standard deviations of the mean, years.(b) Suppose that the distribution is bell-shaped. If approximately 68% of the home buyers' ages lie between 39 years and 59 years, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is .

a)

And that represent 84% of the data within 2.5 deviations from the mean

b) For this case we can assume that the limits between 39 and 59 are given by:

Because within one deviation from the mena we have at least 68% of the data.

And we can solve for the deviation and we got:

Step-by-step explanation:

Part a

Data given  

reprsent the population mean

represent the population standard deviation

The Chebyshev's Theorem states that for any dataset

•We have at least 75% of all the data within two deviations from the mean.

•We have at least 88.9% of all the data within three deviations from the mean.

•We have at least 93.8% of all the data within four deviations from the mean.

Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least:

And if we use the value of k=2.5 we got:

And that represent 84% of the data within 2.5 deviations from the mean

Part b

For this case we can assume that the limits between 39 and 59 are given by:

Because within one deviation from the mena we have at least 68% of the data.

And we can solve for the deviation and we got:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: