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trasher [3.6K]
3 years ago
11

Doña Mercedes' debt can be paid in 32 weeks, as long as $ 50 is paid in the first week, $ 80 in the second week, $ 110 in the th

ird week and so on. What was the amount of her debt?
Mathematics
1 answer:
KengaRu [80]3 years ago
8 0

Answer:

Step-by-step explanation:

21

that is all

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"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the
STALIN [3.7K]

Answer:

\\ P(z>-2) = 0.97725 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:

  1. We are dealing here with <em>normally distributed data</em>, that is "<em>the frequency distribution of the life length data is known to be mound-shaped</em>".
  2. The normal distribution is defined by two parameters: the population mean (\\ \mu) and the population standard deviation (\\ \sigma). In this case, we have that \\ \mu = 55 months, and \\ \sigma = 3 months.
  3. To find the probabilities, we have to use the <em>standard normal distribution</em>, which has \\ \mu = 0 and \\ \sigma = 1. The probabilities for this distribution are collected in the <em>standard normal table</em>, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
  4. For most cases, we need to use the <em>cumulative standard normal table, </em>and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: \\ z = \frac{x - \mu}{\sigma} [1]. A z-score tells us the distance from the mean that a raw score is from it in <em>standard deviations units</em>. If this value is <em>negative</em>, the raw score is <em>below</em> the mean. Conversely, a <em>positive</em> value indicates that it is <em>above</em> the mean.
  5. The <em>cumulative standard normal table </em>is made for positive values of z. Since the normal distribution is <em>symmetrical</em> around the mean, we can find the negative values of z using this formula: \\ P(z [2].

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>.

\\ z = \frac{49 - 55}{3}

\\ z = \frac{-6}{3}

\\ z = -2

This means that the raw score is represented by a z-score of \\ z = -2, 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

\\ P(z

\\ P(z2)

\\ P(z2)

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

\\ P(z>-2) = 1 - P(z

\\ P(z>-2) = 1 - 0.02275

\\ P(z>-2) = 0.97725

That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is

\\ P(z>-2) = 0.97725 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).

6 0
3 years ago
I need help fast<br> w = 3.4cm<br> h = 2.5cm
Vikentia [17]

The width of the insect is 0.17 cm and the height of the insect is 0.125 cm.

Step-by-step explanation:

Step 1:

The scale factor is given by dividing the measurement after scaling by the same measurement

The given drawing of the insect is larger than the actual insect.

The scale factor is 20: 1 which means 20 cm on the drawing is 1 cm on the actual insect.

Step 2:

To obtain the actual insect's dimensions, we divide the dimensions of the drawing by 20.

The width of the actual insect = \frac{3.4}{20} = 0.17.

The height of the actual insect = \frac{2.5}{20} = 0.125.

The width of the insect is 0.17 cm and the height of the insect is 0.125 cm.

7 0
3 years ago
Solve the proportion to determine the value of x4x/15=60/x
frozen [14]
4x/15 = 60/x
4x^2 = 900
x^2 = 225
x = 15 
4 0
3 years ago
Hannah places her home on a grid so that each unit square on the grid equates to 11 mile. She uses the fact that the major stree
Aneli [31]

Answer:

64.1

Step-by-step explanation:

You use Pythagorean theorem which is x^2 +y^2=z^2 (^ this means to the power of) so you would get 55^2+33^2=z^2. solving this would get you z=64.1404708433 or 64.1

8 0
3 years ago
Charlotte has 12 t shirts.one fourth of her t shirts are green. How many of charlottes t shirts are green?
ella [17]
3 T shirts. 12 divided by 4.
7 0
2 years ago
Read 2 more answers
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