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kirill115 [55]
3 years ago
14

It is possible to obtain a ""quick-and-dirty"" estimate of the mean of a normal distribution from the 50th percentile value on a

normal probability plot. Provide an argument why this is so. It is also possible to obtain an estimate of the standard deviation of a normal distribution by subtracting the 84th percentile value from the 50th percentile value. Provide an argument explaining why this is so.
Mathematics
1 answer:
frozen [14]3 years ago
8 0

Answer:

Step-by-step explanation:

It is possible to obtain a ""quick-and-dirty"" estimate of the mean of a normal distribution from the 50th percentile value on a normal probability plot, because normal distribution curve is symmetrical about its mean with 50% on either side of the mean. Also it is unimodal, with mean = median = mode. Because of symmetrical shape, and other special properties we can obtain estimate of mean as the 50th percentile of any normal distribution.

Also in normal distribution 34% lie between mean and 1 std deviation on right side/left side

This gives 84th percentile is got by taking the z value on right side of mean.

When we subtract 84th percentile value from the 50th percentile value we really get -1 times std deviation.  Hence to get std deviation actual value, without negative sign, we subtract (50-34) = 16th percentile from mean.

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The next model of a sports car will cost 4.4% more that the current model. The current model costs $48,000, How much will the pr
podryga [215]

Answer:

$50,112.  Increase is $2,112

Step-by-step explanation:

1st way.  $48,000 x 1.044 = $50,112.  1.044 is the same thing as saying 104.4% of the total price in decimal form, which is what the new price would be when adding 4.4% to the 100% of the original price.  To get the amount of increase just find the difference in the two.  $50,112-$48,000 = $2,112

2nd way.  $48,000 x .044.  =  $2,112 .044 is 4.4% in decimal form. So you found the increase here.  Add the increase to the original price.  $48,000 + $2,112 to get the new price of $50,112.

7 0
3 years ago
26. Law of sines, please give a step by step explanation
Stels [109]

Answer:

  174.6 ft

Step-by-step explanation:

It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)

We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...

  180° -30° -112° = 38°

Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.

  c/sin(C) = a/sin(A)

  c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft

The height of the tree is about 174.6 feet.

5 0
3 years ago
Product of two natural numbers p and q is 590 and their hcf is 59. how many set of values of p and q is possible
djverab [1.8K]

\text{Let the product of two natural numbers p and q is 590, and their HCF is 59}\\
\\
\text{we know that the product of LCM and HCF of any two numbers is equal}\\
\text{to the product of the numbers. that is}\\
\\
\text{HCF}\times \text{ LCM}=p\times q\\
\\
\Rightarrow 59 \times \text{LCM}=590\\
\\
\Rightarrow \text{LCM}=\frac{590}{59}\\
\\
\Rightarrow \text{LCM}=10\\
\\
\text{for any two natural numbers, their Least Common Multiple (LCM) is always}

\text{greater than their HCF.}\\
\\
\text{but here we can see that }LCM

Hence there is no such natural numbers exist.

7 0
3 years ago
Which statement is TRUE concerning the slope of the line formed by the hypotenuse of each triangle?
alex41 [277]

Answer:

it would be

Step-by-step explanation:

I do not think you need an explanation but if so just comment

6 0
3 years ago
a scale drawing of a building needs to be made using the scale 1 in = 190 ft. how tall will the builging in the scale drawing be
Artist 52 [7]

Answer:

\boxed{\text{3 in}}

Step-by-step explanation:

1 in = 190 ft

x in = 570 ft

We can use ratio and proportion to solve this problem.

\begin{array}{cccl}\dfrac{1}{x} & = & \dfrac{190}{570} & \\\\570 & = & 190x & \text{Mutiplied by lowest common denominator (570x)}\\3 & = & x & \text{Divided each side by 3}\\\end{array}

The building will be \boxed{\textbf{3 in}} tall in the scale drawing.

3 0
3 years ago
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