1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Salsk061 [2.6K]
3 years ago
8

A school wishes to accept 2000 students for their freshman class, and they expect 20,000 applications. In order to make their ad

missions decisions very easy, the only criterion they will use is SAT score. So, their goal is to accept a student if and only if their SAT score is in the top 10%. However, because their computer system is so old, the applications only come in one at a time, and they must decide whether to accept or reject before moving on to the next application. Assuming that SAT scores are normally distributed with a mean of 1000 and a standard deviation of 200, how should they set the score threshold to end up with as close to 2000 students as possible? Give your answer first symbolically (in terms of a pdf, cdf, etc), then use a normal distribution table1 to provide a numerical answer.
Mathematics
1 answer:
vovangra [49]3 years ago
3 0

Answer:

456

Step-by-step explanation:

Let X be the SATscore scored by the students

Given that X is normal (1000,200)

By converting into standard normal variate we can say that

z=\frac{x-1000}{200} is N(0,1)

To find the top 10% we consider the 90th percentile for z score

Z 90th percentile = 1.28

X= 200+1.28(200)\\= 200+256\\=456

i.e. only students who scored 456 or above only should be considered.

You might be interested in
Where is the length of a surface area
REY [17]
The first number but it doesn't really matter.
3 0
3 years ago
Read 2 more answers
Let P = 0.50.30.50.7 be the transition matrix for a Markov chain with two states. Let x0 = 0.50.5 be the initial state vector fo
pav-90 [236]

Answer:

Probability distribution vector = \left(\begin{array}{c}0.375\\ 0.625 \end{array} \right)

Step-By-Step Explanation

If P=\left(\begin{array}{cc}0.5&0.3\\ 0.5&0.7 \end{array} \right)  is the transition matrix for a Markov chain with two states.  

x_{0}=\left(\begin{array}{c}0.5\\ 0.5 \end{array} \right)  be the initial state vector for the population.

X_{1}=P x_{0}=\left(\begin{array}{cc}0.5&0.3\\ 0.5&0.7 \end{array} \right) \left(\begin{array}{c}0.5\\ 0.5 \end{array} \right) =\left(\begin{array}{c}0.4\\ 0.6 \end{array} \right)  

X_{2}=P^{2} x_{0}=\left(\begin{array}{c}0.38\\ 0.62 \end{array} \right)  

X_{3}=P^{3} x_{0}=\left(\begin{array}{c}0.38\\ 0.62 \end{array} \right)  

X_{30}=P^{30} x_{0}=\left(\begin{array}{c}0.37499\\ 0.625 \end{array} \right)  

In the long run, the probability distribution vector Xm approaches the probability distribution vector \left(\begin{array}{c}0.375\\ 0.625 \end{array} \right) .

This is called the steady-state (or limiting,) distribution vector.

4 0
3 years ago
Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority
Andre45 [30]

Answer:

The 95% confidence interval of  the true proportion of all Americans who are in favor of gun control legislation is (0.5471, 0.5779).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. This means that n = 4000 and \pi = \frac{2250}{4000} = 0.5625

Estimate the true proportion of all Americans who are in favor of gun control legislation using a 95% confidence interval

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5625 - 1.96\sqrt{\frac{0.5625*0.4375}{4000}} = 0.5471

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5625 + 1.96\sqrt{\frac{0.5625*0.4375}{4000}} = 0.5779

The 95% confidence interval of  the true proportion of all Americans who are in favor of gun control legislation is (0.5471, 0.5779).

8 0
3 years ago
Create an exponential to describe $100 at 2% interest compounded annually for x years
zysi [14]

Answer:

A=100(1.02)^{x}                  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=x\ years\\ P=\$100\\ r=2\%=2/100=0.02\\n=1  

substitute in the formula above

A=100(1+\frac{0.02}{1})^{1*x}  

A=100(1.02)^{x}  

8 0
3 years ago
Please Help! Answer the question on this picture!
Debora [2.8K]

Answer:

it dilated by two

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Need help with 25 and 26 plz
    12·1 answer
  • How do I solve this ?
    8·1 answer
  • The ratio of pens to pencils in Mrs. Bosworth's desk is 3:1. What does this mean?
    15·1 answer
  • Determine whether a triangle can be formed with the given side lengths.
    11·1 answer
  • What is the solution to the equation?
    9·1 answer
  • A sandbox is 2.5 m wide and 3.5m long<br>how much does it take to fill 0.3 m height.​
    9·1 answer
  • Use compatible numbers to estimate the quotient. <br> 522 divided by 6 please help!!!
    12·1 answer
  • Can someone please help me, im stuck. ​
    15·2 answers
  • A group of students were surveyed to find out if they like watching television or reading during their free time. The results of
    5·1 answer
  • El número 9 es un número primo?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!