A factory uses a special kind of lubricant to maintain its four milling machines. The weekly lubricant usage for each machine can be approximated with a normal distribution. This distribution has a mean of 30 gallons and a standard deviation of 11.5 gallons, and it can be considered as an independent random variable (zero covariance, zero correlation) from machine to machine. Suppose at the beginning of the week, the factory has a total of 150 gallons of lubricant in stock. The factory will not receive any replenishment of lubricant from its supplier until the end of the week. Assume that the total lubricant usage (four machines combined) also follows a normal distribution. Required:
What is the probability that the factory will run out of lubricant before the next replenishment arrives?

0.0968 = 9.68% probability that the factory will run out of lubricant before the next replenishment arrives

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

This distribution has a mean of 30 gallons and a standard deviation of 11.5 gallons

Since there are four machines, we have that:

What is the probability that the factory will run out of lubricant before the next replenishment arrives?

More than 150 gallons, so this is 1 subtracted by the pvalue of Z when X = 50.

has a pvalue of 0.9032

1 - 0.9032 = 0.0968

0.0968 = 9.68% probability that the factory will run out of lubricant before the next replenishment arrives

i believe it is c.y = 9x

rise over run. 9 units up over 1 unit right or 9/1

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: