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3 years ago

The sum of three consecutive numbers is 46. Find the

Mathematics

2 answers:

-Dominant- [34]3 years ago

8 0

X
x+1
x+2
x+x+1+x+2=46
3x+3=46
3x=43
x=43/3
x∉{N}
the task is given with a mistake!

Citrus2011 [14]3 years ago

6 0

Let the three consecutive number be x,x+1 and x+2.

It is given sum of three consecutive numbers is 46.

So,x+x+1+x+2=46

3x+3=46.

Subtracting 3 both sides

3x=46-3

3x=43.

x= $\frac{43}{3}.$

Since $\frac{43}{3}.$ is not an integer there is no true answer to this problem.

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Question Help Scores of an IQ test have a bell-shaped distribution with a mean of 100100 and a standard deviation of 1010. Use

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a) 95% percentage of people has an IQ score between 80 and 120.

b) 68% percentage of people has an IQ score between 90 and 110.

c) 2.5% percentage of people has an IQ score greater than 120.

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The empirical formula states that:

The empirical rule is known as the three-sigma rule or 68-95-99.7 rule.
It is a rule which states that for a normal distribution, almost all data falls within three standard deviations of the mean.
68% of data falls within the first standard deviation that is $\mu \pm \sigma$

95% of data falls within the second standard deviation that is $\mu \pm 2\sigma$

99.7% of data falls within the third standard deviation that is $\mu \pm 3\sigma$

a) percentage of people has an IQ score between 80 and 120

(80, 120) can be written as:

$(80, 120) = (100-2(10), 100 + 2(10))\\= (\mu \pm 2\sigma)$

Thus, it is the interval within two standard deviation from the mean.

Thus, by empirical formula, 95% percentage of people has an IQ score between 80 and 120.

b) percentage of people has an IQ score between 90 and 110

(90, 110) can be written as:

$(90, 110) = (100-1(10), 100 + 1(10))\\= (\mu \pm 1\sigma)$

Thus, it is the interval within one standard deviation from the mean.

Thus, by empirical formula, 68% percentage of people has an IQ score between 90 and 110.

c) P(score greater than 120)

= 1 - percentage of score less than 80 - percentage of score between 80 and 120

$= 1 - (95\% + 2.5\%) = 2.5\%$

From empirical formula,

2.5% percentage of people has an IQ score greater than 120.

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