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
ArbitrLikvidat [17]
3 years ago
13

A company compiles data on a variety of issues in education. In 2004 the company reported that the national college​ freshman-to

-sophomore retention rate was 66​%. Consider colleges with freshman classes of 500 students. Use the​ 68-95-99.7 rule to describe the sampling distribution model for the percentage of students expected to return for their sophomore years. Do you think the appropriate conditions are​ met
Mathematics
1 answer:
nasty-shy [4]3 years ago
8 0

Answer:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

And we have :

\mu_p = 0.66

\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212

Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

Step-by-step explanation:

For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.

We want to know if we can apply the normal approximation, so we need to check 3 conditions:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

And we have :

\mu_p = 0.66

\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212

And we can use the empirical rule to describe the distribution of percentages.

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

You might be interested in
Please answer to those<br><br> (a+2)(a+2)<br><br> (b+7)(b+7)<br><br> (c-3)(c-3)
oksano4ka [1.4K]

Answer:   1. a^2 + 4a + 4

                2. b^2 + 14b + 14

                3. c^2 -6c + 9



5 0
3 years ago
Read 2 more answers
Sin46=8/x 20 POINTS need asap
hodyreva [135]

Answer:

x = 11.12130872

Step-by-step explanation:

if this isnt right then let me know

6 0
3 years ago
25 × 13 = __________ twenty-fives. 49 × 11 = __________ elevens.
andreyandreev [35.5K]

Answer:

I hope this helps. I don't quite know what you're looking for.

Step-by-step explanation:

25 x 13 = 325

325 divided by 25

= 13 twenty fifths.

49 x 11 = 539

539 divided by 11

= 49 elevenths

8 0
2 years ago
An ancient Chinese candle clock tells the amount of time that has passed by the amount of wax that has been melted off the candl
rjkz [21]
Two candles=8 hours=8*60=480 minutes
4 inch is 4/12 of a candle, 4/12 of 4 hours=16/12=4/3 hours=80 minutes
so the total minutes are 480+80=560 
8 0
3 years ago
Read 2 more answers
Solve -6x+3less than equal to 21
mylen [45]

Answer: -3

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • a car dealership has 75 cars on the lot. Of the cars, 40% are black. how many black cars are on the lot?​
    5·2 answers
  • What are the ordered pair solutions for the system below?
    11·1 answer
  • Harvard University accepts 6 students for every 100 applicants. How many students will be accepted if 850 applicants apply for a
    7·2 answers
  • While on a car trip with her family,Erin saw a sign that read,"Amarillo 100 miles,Lubbock 80 miles". She concluded that the dist
    8·2 answers
  • What is the answer A, B, C, or D
    8·1 answer
  • Write these equations in y=mx+b form....
    14·1 answer
  • 2.85 as a mixed number
    10·2 answers
  • A boy walks 5 ķm at vkm/hr. He then cycles 15 km at 2v km/hr. In terms of v, write down the time taken in hours
    10·1 answer
  • PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
    7·1 answer
  • U should donate to khan academy: )
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!