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likoan [24]
3 years ago
12

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule t

o determine the following. A.) what percentage of people has an IQ between 64 and 136? B.) what percentage of people has an IQ score less than 76 or greater than 124? C.) what percentage of people has an IQ score greater than 112?
Mathematics
1 answer:
MissTica3 years ago
8 0

Answer:

A) 99.7% of people have an IQ between 64 and 136.

B) 5% of people have an IQ score less than 76 or greater than 124.

C) 16% of people have an IQ score greater than 112.

Step-by-step explanation:

The Empirical Rule tells us that, in a normal or 'bell-shaped' distribution, 68% of the data is one standard deviation from the mean, 95% of the data is two standard deviations from the mean, and 99.7% of the data is three standard deviations from the mean.

A) 64 and 136 are 3 standard deviations away from the mean, so 99.7% of people have an IQ between 64 and 136.

B) 76 and 124 are 2 standard devations away from the mean, but the answer is asking what percentage is not between them. 100% - 95% gives us 5%.

C) 112 is one standard deviation away from the mean. If we want to find the percentage greater, then we can do 100% - 50% (as 112 is to the left of the mean), then we can take half of 68 to get 34%, and after subtracting 50% and 34% from the 100%, we get 16%.

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What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with vertices L(0,-3), M(-2,1), N(1,5), O(3
ArbitrLikvidat [17]
ANSWER

\boxed {( \frac{1}{2} , 1)}

EXPLANATION

The given parallelogram has vertices,

L(0,-3), M(-2,1), N(1,5), O(3,1).

The diagonals of the parallelogram bisect each other.

From the diagram, we can see that, the diagonals have coordinates L(0,-3),N(1,5)

and

M(-2,1),O(3,1).

The midpoint of any of the diagonals will give us the coordinates of intersection of the diagonals.

Recall the midpoint formula,

(\frac{x_1+x_2}{2}, \frac{y_2+y_1}{2})

Using L(0,-3),N(1,5) gives,

(\frac{0+1}{2}, \frac{ - 3+5}{2})

(\frac{1}{2}, \frac{ 2}{2})

(\frac{1}{2}, 1)

Or we could have also used,M(-2,1),O(3,1) to get,

(\frac{-2+3}{2}, \frac{ 1+1}{2})

(\frac{ 1}{2}, \frac{ 2}{2})

(\frac{ 1}{2}, 1)

The correct answer is C

6 0
3 years ago
Use the normal distribution of SAT critical reading scores for which the mean is 502 and the standard deviation is 116. Assume t
PSYCHO15rus [73]

Answer:

(a) 93.19%

(b) 267.3

Step-by-step explanation:

The population mean and standard deviation are given as 502 and 116 respectively.

Consider, <em>X</em> be the random variable that shows the SAT critical reading score is normally distributed.

(a) The percent of the SAT verbal scores are less than 675 can be calculated as:

P(X

Thus, the required percentage is 93.19%

(b)

The number of SAT verbal scores that are expected to be greater than 575 can be calculated as:

P(X>575)=P(\frac{x-502}{116}>\frac{575-502}{116}\\P(X>575)=P(Z>\frac{575-502}{116})\\P(X>575)=P(Z>0.6293)\\P(X>575)=0.2673

So,

Out of 1000 randomly selected SAT verbal scores, 1000(0.2673) = 267.3 are expected to have greater than 575.

8 0
2 years ago
250 divided by 10 to the 2 nd power
laila [671]
The answer to your problem is 2.5.
5 0
3 years ago
Read 2 more answers
9. A ranch has 575 cows on 25 acres of land. Which rate best represents the relationship
Vitek1552 [10]

Answer:

10/10

Step-by-step explanation:

7 0
3 years ago
I need help please?!!!!!!
Vadim26 [7]

Answer:

simplified is

x ^5 y ^15 z ^10

Step-by-step explanation:

3 0
3 years ago
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