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makvit [3.9K]
1 year ago
12

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. use empirical rule to de

termine the following:
a) what percentage of people has an IQ score between 61 and 139?
b) what percentage of people has IQ score less than 87 or greater than 113?
c) what percentage of people has an IQ score greater than 113?
Mathematics
1 answer:
azamat1 year ago
5 0

Using the Empirical Rule, the percentages are given as follows:

a) 99.7%.

b) 32%.

c) 16%.

<h3>What does the Empirical Rule state?</h3>

It states that, for a normally distributed random variable:

  • Approximately 68% of the measures are within 1 standard deviation of the mean.
  • Approximately 95% of the measures are within 2 standard deviations of  the mean.
  • Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Item a:

61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.

Item b:

87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.

Item c:

Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.

More can be learned about the Empirical Rule at brainly.com/question/24537145

#SPJ1

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Answer:

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Step-by-step explanation:

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so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

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so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13

49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13

we can solve these two equation using the elimination method, by simply adding the two equations

\quad\quad49a-7b=-13\\+\quad49a+7b=-13

------------------------------

\quad\quad 98a=-26

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Now we can plug this value of a in any of the two equations.

49a-7b=-13

49\left(-\dfrac{13}{49}\right)-7b=-13

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b=0

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

y=\left(-\dfrac{13}{49}\right)x^2+0x+0

y=-\dfrac{13}{49}x^2

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This our equation of the arch!

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