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7nadin3 [17]
3 years ago
8

Question 5 Unsaved

Mathematics
1 answer:
Otrada [13]3 years ago
3 0

We can use the compound interest formula

F=P(1+i)^n

where

F=Future value of investment to be found

P=present value of investment ($1000)

i=interest per period (1/4 year)=0.04/4=0.01

n=number of periods (3 years * 4 quarters = 12)


Substitute or "Plug in" values, so to speak,

F=1000*(1+0.01)^12

use a calculator to do the sum

=1126.83 (to the nearest cent, and use the proper rounding rules)



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The sum of the angle measures of a triangle is 180°. Find the value of x. Then find the angle measures of the triangle.
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The sum of the angles is ...

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Considering the number of questions incorrect from classmates on a quiz {10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19,
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Answer:

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

Step-by-step explanation:

We are given the following data in the question:

10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{225}{15} = 15

Sum of squares of differences = 25 + 16 + 9 + 4 + 4+ 4 + 1 + 0+ 1+ 1 + 4 + 9 + 9+ 16 + 25 = 128

S.D = \sqrt{\dfrac{128}{14}} = 3.02

Empirical rule:

  • According to this rule almost all the data lies within three standard deviation of the mean for a normal distribution.
  • About 68% of data lies within one standard deviation of the mean.
  • About 95% of data lies within two standard deviations of mean.
  • Arround 99.7% of data lies within three standard deviation of mean.

Thus, by empirical rule,

\mu \pm 1\sigma = 15\pm (3.02) = (11.98,18.02)

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

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