Dividing two decimals means that we need to make the following math operation:
According to the following definition:
We can prove that our result is correct by multiplying the divisor by the quotient plus the reminder and verifying that this result matches the dividend. Also, we can use a calculator to prove that.
Answer:
y = 2x
Step-by-step explanation:
Slope =
Answer:
or P(x>49) is about 97.725% (or being less precise 97.5% using the <em>empirical rule</em>).
Step-by-step explanation:
We solve this question using the following information:
Having all this information, we can solve the question.
<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3><em>First Step: Use formula [1] to find the z-score of the raw score x = 49 months</em>.
This means that the raw score is represented by a z-score of , which tells us that it is<em> two standard deviations below</em> the population mean.
<em>Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.</em>
For a z = 2, the probability is 0.97725.
Then
But we <em>are not asked</em> for P(z<-2) but for P(z>-2) = P(x>49). This probability is the <em>complement</em> of the previous result, that is
That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is
or about 97.725%
A graph below shows this result.
Notice that if we had used the <em>68-95-99.7 rule</em> (also known as the <em>empirical rule</em>), that is, in a normal distribution, the interval between <em>one standard deviation below and above the mean</em> contains, approximately, 68% of the observations; the interval between <em>two standard deviations below and above the mean</em> contains, approximately, 95% of the observations; and the interval between <em>three standard deviations</em> below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last <em>less</em> than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.
We can conclude that with a less precise answer (but faster) because of the <em>symmetry of the normal distribution</em>, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).
