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Eva8 [605]
3 years ago
5

Which is the reflection line for the transformation

Mathematics
1 answer:
Alik [6]3 years ago
5 0

Step-by-step explanation:

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Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is t
svet-max [94.6K]

Answer:

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 450, \sigma = 100

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

Z = \frac{X - \mu}{\sigma}

Z = \frac{550 - 450}{100}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 350

Z = \frac{X - \mu}{\sigma}

Z = \frac{350 - 450}{100}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

Z = \frac{X - \mu}{\sigma}

1.88 = \frac{X - 450}{100}

X - 450 = 1.88*100

X = 638

A score of 638(or higher).

c. Find the 60th percentile of the test scores.

X when Z has a pvalue of 0.60. So it is X when Z = 0.253

Z = \frac{X - \mu}{\sigma}

0.253 = \frac{X - 450}{100}

X - 450 = 0.253*100

X = 475.3

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

Z = \frac{X - \mu}{\sigma}

-0.385 = \frac{X - 450}{100}

X - 450 = -0.385*100

X = 411.5

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

Z = \frac{X - \mu}{\sigma}

0.385 = \frac{X - 450}{100}

X - 450 = 0.385*100

X = 488.5

The middle 30% of the test scores is between 411.5 and 488.5.

7 0
3 years ago
What is the completely factored form of p4 – 16? (p – 2)(p – 2)(p 2)(p 2) (p – 2)(p – 2)(p – 2)(p – 2) (p minus 2) (p 2) (p squa
n200080 [17]

The completely factored form of the provided polynomial is  (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

<h3>What is polynomial?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is a real number).

The polynomial equation given in the problem is,

p^4 - 16

Let the factor form of the polynomial is f(p). Thus,

f(p)=p^4 - 16\\f(p)=p^4 - 2^4\\f(p)=(p^2)^2- (2^2)^2

Using the formula of difference of squares, we get,

f(p)=(p^2-4)(p^2+4)\\f(p)=(p^2-2^2)(p^2+4)\\f(p)=(p-2)(p+2)(p^2+4)

Thus, the completely factored form of the provided polynomial is  (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

Learn more about polynomial here;

brainly.com/question/24380382

3 0
2 years ago
PLS HELP 10 brain list
loris [4]

Answer:

y:))))))))))))))))))))

6 0
2 years ago
Find the power of 3/8^3
GREYUIT [131]

(3/8)³ = (3/8)(3/8)(3/8)

Multiply across:

(3/8) x (3/8) = 9/64

Simplify:

(9/64)(3/8) = 27/512

27/512 is your fraction answer (cannot be reduced).

To find the decimal answer, divide:

27/512 = 0.05

0.05 (rounded) is your decimal answer

hope this helps

3 0
3 years ago
What are the period and amplitude of the function?
Marta_Voda [28]

Answer: it’s a

Step-by-step explanation:

7 0
3 years ago
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