a local pizzeria sold 65 pizzas yesterday.(a) the owner offers the employees a bonus if the number of pizza increased by 20 pers
1 answer:
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Answer:
Step-by-step explanation:
In essence, one needs to work their way backwards to solve this problem. Use the information to construct the function.
The function has verticle asymptotes at (x = 4) and (x = 5). This means that the denominator must have (x - 4) and (x - 5) in it. This is because a verticle asymptote indicates that the function cannot have a value at these points, the function jumps at these points. This is because the denominator of a fraction cannot be (0), the values (x - 4) and (x - 5) ensure this. Since if (x) equals (4) or (5) in this situation, the denominator would be (0) because of the zero product property (this states that any number times zero equals zero). So far we have assembled the function as the following:
The function has x-intercepts at (6, 0), and (0, 10). This means that the numerator must equal (0) when (x) is (6) or (10). Using similar logic that was applied to find the denominator, one can conclude that the numerator must be (). Now one has this much of the function assembled
Finally one has to include the y-intercept of (0, 120). Currently, the y-intercept is (60). This is found by multiplying the constants together. (6 * 10) equals (60). One has to multiply this by (2) to get (120). Therefore, one must multiply the numerator by (2) in order to make the y-intercept (120). Thus the final function is the following:
Answer:
a. The positive difference between Nelson's height and the population mean is: .
b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).
c. Nelson's z-score: (Nelson's height is <em>below</em> the population's mean 1.174 standard deviations units).
d. Nelson's height is <em>usual</em> since .
Step-by-step explanation:
The key concept to answer this question is the z-score. A <em>z-score</em> "tells us" the distance from the population's mean of a raw score in <em>standard deviation</em> units. A <em>positive value</em> for a z-score indicates that the raw score is <em>above</em> the population mean, whereas a <em>negative value</em> tells us that the raw score is <em>below</em> the population mean. The formula to obtain this <em>z-score</em> is as follows:
[1]
Where
is the <em>z-score</em>.
is the <em>population mean</em>.
is the <em>population standard deviation</em>.
From the question, we have that:
- Nelson's height is 68 in. In this case, the raw score is 68 in
in.
in.
in.
With all this information, we are ready to answer the next questions:
a. What is the positive difference between Nelson's height and the mean?
The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):
.
That is, <em>the positive difference is 2.7 in</em>.
b. How many standard deviations is that [the difference found in part (a)]?
To find how many <em>standard deviations</em> is that, we need to divide that difference by the <em>population standard deviation</em>. That is:
In words, the difference found in part (a) is 1.174 <em>standard deviations</em> from the mean. Notice that we are not taking into account here if the raw score, <em>x,</em> is <em>below</em> or <em>above</em> the mean.
c. Convert Nelson's height to a z score.
Using formula [1], we have
This z-score "tells us" that Nelson's height is <em>1.174 standard deviations</em> <em>below</em> the population mean (notice the negative symbol in the above result), i.e., Nelson's height is <em>below</em> the mean for heights in the club presidents of the past century 1.174 standard deviations units.
d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?
Carefully looking at Nelson's height, we notice that it is between those z-scores, because:
Then, Nelson's height is <em>usual</em> according to that statement.