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LUCKY_DIMON [66]
3 years ago
12

For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 50

5 and a standard deviation of 170. The grading process of this year's exam has just begun. The average score of the 35 exams graded so far is 530.What is the probability that a sample of 35 exams will have a mean score of 530 or more if the exam scores follow the same distribution as in the past?
Mathematics
1 answer:
Volgvan3 years ago
3 0

Answer:

P(\bar X>530)=1-0.808=0.192

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the scores, and for this case we know the distribution for X is given by:

X \sim N(\mu=505,\sigma=170)  

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

On this case  \bar X \sim N(505,\frac{170}{\sqrt{35}})

2) Calculate the probability

We want this probability:

P(\bar X>530)=1-P(\bar X

The best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

If we apply this formula to our probability we got this:

P(\bar X >530)=1-P(Z

P(\bar X>530)=1-0.808=0.192

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Answer:  The answer is in the attached figure.


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As given in the question, a rectangular prism ABCDEFGH is drawn in the attached figure, where length is 8 units, width is 2 units and height is 3 units.


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3 years ago
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Transformation which can be used for mapping of one triangle to another are;

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8 0
2 years ago
what is the equation in slope form of the line that is parallel to the given line and passes through the point (-3,1)​
viktelen [127]

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate the slope of the given line using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = \frac{2+4}{2+2} = \frac{6}{4} = \frac{3}{2}

Parallel lines have equal slopes and using (a, b) = (- 3, 1), then

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y - 1 = \frac{3}{2}(x + 3) ← in point- slope form

6 0
3 years ago
What is the value of x?<br><br><br> 68<br><br> 32<br><br> 54<br><br> 36
Dovator [93]

Answer:

A) 68

Step-by-step explanation:

Use the <em>Exterior Angle Theorem</em>.

The Exterior Angle theorem states that the exterior angle's measurement will be equal that of the two opposite interior angles.

Set the equation. Note that you are given the exterior angle and one interior angle:

58 + x = 126

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 58 from both sides of the equation:

x + 58 (-58) = 126 (-58)

x = 126 - 58

x = 68

A) 68 is your answer.

~

4 0
2 years ago
Read 2 more answers
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