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
sukhopar [10]
3 years ago
10

The scores of individual students on the American College Testing (ACT) Program College Entrance Exam have a normal distribution

with mean 18.6 and standard deviation 6.0. At Westside High, 400 students take the test. Assume their scores are all independent. If the scores at this school have the same distribution as nationally, the probability that the average of the scores of all 400 students exceeds 19.0 is smaller than the probability that a single student has a score exceeding 19.0 larger than the probability that a single student has a score exceeding 19.0 the same as the probability that a single student has a score exceeding 19.0
Mathematics
1 answer:
tekilochka [14]3 years ago
7 0

Answer:

The probability that the average of the scores of all 400 students exceeds 19.0 is larger than the probability that a single student has a score exceeding 19.0

Step-by-step explanation:

Xi~N(18.6, 6.0), n=400, Yi~Ber(p); Z~N(0, 1);

P(0\leq X\leq 19.0)=P(\frac{0-\mu}{\sigma} \leq \frac{X-\mu}{\sigma}\leq \frac{19-\mu}{\sigma}), Z= \frac{X-\mu}{\sigma}, \mu=18.6, \sigma=6.0

P(-3.1\leq Z\leq 0.0667)=\Phi(0.0667)-\Phi (-3.1)=\Phi(0.0667)-(1-\Phi (3.1))=0.52790+0.99903-1=0.52693

P(Xi≥19.0)=0.473

\{Yi=0, Xi<  19\\Yi=1, Xi\geq  19\}

p=0.473

Yi~Ber(0.473)

P(\frac{1}{n}\displaystyle\sum_{i=1}^{n}X_i\geq 19)=P(\displaystyle\sum_{i=1}^{400}X_i\geq 7600)

Based on the Central Limit Theorem:

\displaystyle\sum_{i=1}^{n}X_i\~{}N(n\mu, \sqrt{n}\sigma),\displaystyle\sum_{i=1}^{400}X_i\~{}N(7440, 372)

Then:

P(\displaystyle\sum_{i=1}^{400}X_i\geq 7600)=1-P(0

P(\displaystyle\sum_{i=1}^{n}Y_i=1)=P(\displaystyle\sum_{i=1}^{400}Y_i=1)

Based on the Central Limit Theorem:

\displaystyle\sum_{i=1}^{400}Y_i\~{}N(400\times 0.473, \sqrt{400}\times 0.499)=\displaystyle\sum_{i=1}^{400}Y_i\~{}N(189.2; 9.98)

P(\displaystyle\sum_{i=1}^{400}Y_i=1)\~{=}P(0.5

Then:

the probability that the average of the scores of all 400 students exceeds 19.0 is larger than the probability that a single student has a score exceeding 19.0

You might be interested in
Gina made 9,350 mL of chicken noodle soup. She packed 1.8 L of the soup in her kids' lunches. She froze the rest of the soup.
Alika [10]
It is 7,550 milliliters
3 0
3 years ago
Read 2 more answers
Given that f:x→ax+b and f²:x→4x+9, find the value of the constants a and b​
zimovet [89]

Answer:

Step-by-step explanation:  

hello :

ax+b =4x+9     so a=4 and b=9

4 0
3 years ago
In art class mrsJocelyn gave everyone a 1 foot stick to measure and cut Vivian measured and cut her stick into 5 equal pieces Sc
garri49 [273]
Idk sorry i cant help

hope this helps XD
6 0
3 years ago
Negative X squared minus 2X minus 6<br> X^2-2X-6
mojhsa [17]
-x^2 -2x-6
Multiply everything by negative one to make X positive
X^2+2x+6

Use quadratic formula
-2+-sq rt of 2^2-4(1)(6) / 2
-2+-sqrt of -20 /2
-2+ 2i/2. -2-2i/2
-2+i. -2-i
5 0
3 years ago
How to estimate 96 Times 34 what is the answer
Marrrta [24]

When it says to estimate, I always think of doing it by hand to show work.  So set it up like this:

  96

<u>x 34</u>

So follow it out multiplying across 4*6 and 4*9 carrying over as needed to get it to look like this:

  96

<u>x 34</u>

384


Do the same for the 3 to get this:

  96

<u>x 34</u>

  384

2880

Add 384+2880=3264

Your final answer is 3,264

6 0
3 years ago
Other questions:
  • What is the degree of the sin of .19
    8·1 answer
  • The sides of a triangle are in the ratio 2:3:5. The perimeter of the triangle is 55
    11·1 answer
  • Write a decimal subtraction problem that requires regrouping to solve. then solve the problem
    10·1 answer
  • Please help with surface area
    10·2 answers
  • Which best describes a system of equations that has no solution?
    10·1 answer
  • Here is a list of numbers:<br> 14, 4, 4, 16, 14, 3, 13 ,11 ,1 ,8<br> State the median.
    7·1 answer
  • 4 (x-9) = -48 x= please help me <br>​
    8·1 answer
  • 9 less than the square root of a number and 3
    11·1 answer
  • Hey, I need some answers!!<br> What is 16-2t = 5t + 9?
    12·1 answer
  • Factor 7/10 out of 7/10z+21.<br><br> 7/10z+21=
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!