Geomtry question pls help !!!

Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is approximately normal with a mean of 500

Artist 52 [7]

Answer:

a) Due to the higher z-score, Ronald performed better relative to his peers on the test.

b) Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.

c) 95% of the population fall between graded of 4.868 and 31.132 on the ACT.

95% of the population fall between graded of 304 and 696 on the SAT.

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use 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 question:

(a) Relative to their peers who also took the tests, who performed better on his test? Explain.

We have to find whoever has the higher z-score.

Ronald:

Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is approximately normal with a mean of 500 and a standard deviation of 100. So the z-score is found when $X = 700, \mu = 500, \sigma = 100$ . So

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

$Z = \frac{700 - 500}{100}$

$Z = 2$

Rubin:

Rubin takes the ACT math exam and scores 31 on the math portion. ACT scores are approximately normally distributed with a mean of 18 and a standard deviation of 6.7. So the z-score is found when $X = 31, \mu = 18, \sigma = 6.7$ . So

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

$Z = \frac{31 - 18}{6.7}$

$Z = 1.94$

Due to the higher z-score, Ronald performed better relative to his peers on the test.

(b) A certain school will only consider those students who score in the top 1% in the math section. What grades would Ronald and Rubin have to receive on their respective tests to be considered for admission?

They have to be in the 100 - 1 = 99th percentile, that is, they need a z-score with a pvalue of at least 0.99. So we need to find for them X when Z = 2.325.

Ronald:

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

$2.325 = \frac{X - 500}{100}$

$X - 500 = 232.5$

$X = 732.5$

Rubin:

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

$2.325 = \frac{X - 18}{6.7}$

$X - 18 = 15.58$

$X = 33.58$

Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.

(c) Between what two grades does 95% of the population fall for the ACT and the SAT exams?

They fall between the 100 - (95/2) = 2.5th percentile and the 100 + (95/2) = 97.5th percentile, that is, they fall between X when Z = -1.96 and X when Z = 1.96.

ACT:

Lower bound:

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

$-1.96 = \frac{X - 18}{6.7}$

$X - 18 = -1.96*6.7$

$X = 4.868$

Upper bound:

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

$1.96 = \frac{X - 18}{6.7}$

$X - 18 = 1.96*6.7$

$X = 31.132$

95% of the population fall between graded of 4.868 and 31.132 on the ACT.

SAT:

Lower bound:

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

$-1.96 = \frac{X - 500}{100}$

$X - 500 = -196$

$X = 304$

Upper bound:

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

$1.96 = \frac{X - 500}{100}$

$X - 500 = 196$

$X = 696$

95% of the population fall between graded of 304 and 696 on the SAT.

7 0

3 years ago

1+1= <br><br> PLEASE HELP!!!!!!

kykrilka [37]

Answer:

2

Step-by-step explanation:

1+1=2 duhhhhhhhhhhhh

3 0

4 years ago

What is the largest prime less then 120

sattari [20]

Answer:

113.

Step-by-step explanation:

119 is divisible by 7.

117 is divisible by 3.

I think it's 113.

If you use your calculator to divide 113 by odd numbers up to 57 you can check if it is prime. You stop at 57 because 57*2 = 114. You need not divide by any number ending in 5 because 113 ends in 3.

I have done this and can't find a quotient that is a whole number so it must be prime (unless I've made a mistake!).

4 0

4 years ago

After 1 year, the value of a car decreases by 19%. The car is now worth £3078. What was the value of the car originally?

Paha777 [63]

Answer:

3800

Step-by-step explanation:

Variables:

O - Original cost

N - New cost

c - change factor

Step 1:

Recognize that if something decreases by 19%, it is worth 19% <em>less</em>

This means that the new price, fractionally, is 100% - 19% = 81%

So we can use c as 0.81 (81/100)

Step 2:

Write an equation to represent what is happening

N = O * c

Step 3:

Sub in what we know

3078 = O * 0.81

Step 4:

Rearange and solve

O = 3078 / 0.81 = 3800

5 0

3 years ago

Every orthogonal matrix is invertible. O True O False

scZoUnD [109]

Answer:

True

Step-by-step explanation:

Every orthogonal matrix is invertible. This is a true statement.

Orthogonal matrices are square matrix whose rows and columns are orthogonal unit vectors.

In an orthogonal matrix columns are linearly independent and since the columns are linearly independent the matrix will be matrix will be invertible. This is according to invertible matrix theorem.

7 0

4 years ago