The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 65 and a standard deviation of 8. Using the empirical (68-95-99.7) rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 57 and 89?

83.85% of 1-mile long roadways with potholes numbering between 57 and 89

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 65

Standard deviation = 8

Using the empirical (68-95-99.7) rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 57 and 89?

It is important to remember that the normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are avobe.

57 = 65 - 8

So 57 is one standard deviation below the mean.

By the Empirical Rule, 68% of the 50% below the mean is within 1 standard deviation of the mean.

89 = 65 + 3*8

So 89 is three standard deviations above the mean.

By the Empirical Rule, 99.7% of the 50% above the mean is within 3 standard deviations of the mean.

0.68*0.5 + 0.997*0.5 = 0.8385

83.85% of 1-mile long roadways with potholes numbering between 57 and 89

step-by-step explanation:

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: