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
OlgaM077 [116]
3 years ago
8

Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education. In 2004 the company repor

ted that the national college freshman-to-sophomore retention rate held steady at 74% over the previous four years.
1. Consider random samples of 400 freshmen who took the ACT. Use the 68-95-99.7 Rule to describe the sampling distribution model for the percentage of those students we expect to return to that school for their sophomore years. Do you think the appropriate conditions are met?
Mathematics
1 answer:
GarryVolchara [31]3 years ago
5 0

Answer:

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806

99.7% of the rates are expected to be betwen 0.674 and 0.806

Step-by-step explanation:

Check for conditions

For this case in order to use the normal distribution for this case or the 68-95-99.7% rule we need to satisfy 3 conditions:

a) Independence : we assume that the random sample of 400 students each student is independent from the other.

b) 10% condition: We assume that the sample size on this case 400 is less than 10% of the real population size.

c) np= 400*0.74= 296>10

n(1-p) = 400*(1-0.74)=104>10

So then we have all the conditions satisfied.

Solution to the problem

For this case we know that the distribution for the population proportion is given by:

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

So then:

\mu_p = 0.74

\sigma_p =\sqrt{\frac{0.74(1-0.74)}{400}}=0.0219

The empirical rule, also referred to as the 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). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806

99.7% of the rates are expected to be betwen 0.674 and 0.806

You might be interested in
Policeman A and Policeman B hand out 70 speeding tickets in a month.
Inessa05 [86]

Answer:

Policeman A = 56 tickets

Step-by-step explanation:

Policemen A + B = 70

If Policeman B hands out x no of tickets...

Then Policeman A hands out 4x no of tickets

meaning...

x + 4x = 70

5x = 70

x = 70/5

x = 14

Therefore Policeman A hands out..

4x = 4 × 14 = 56 tickets

8 0
3 years ago
How do you write 228 o/o as a fraction
sweet-ann [11.9K]
Well I'm assuming you mean percent by o/o
Percentages are out of a hundred so you would write it 228/100
7 0
3 years ago
If a sprinkler Waters 1/20 of a lawn in 1/5 of an hour, how much time will it take to water the entire lawn?
loris [4]
4hrs, I think, because 20 divided by 5 is 4.
6 0
2 years ago
Alicia is writing the program for a video game.
ICE Princess25 [194]

Step-by-step explanation:

<u>A.-6-3 = -9</u>

0+4 = 4  

(-9,4)

<u>B.3-3 = 0</u>

-4+4 = 0  

(0,0)

7 0
3 years ago
Zx and Zy are supplementary angles. Zy measures 108°,
gulaghasi [49]

Answer:

72°

Step-by-step explanation:

Given

Zy = 108°

Zx = ?

We know

Zx + Zy = 180° {being supplementary angles }

Zx + 108° = 180°

Zx = 180° - 108°

Zx = 72°

Hope it will help :)

4 0
3 years ago
Other questions:
  • I need help...Idk what to do because this is all it gave me.
    9·1 answer
  • A number is randomly picked from this list: 2 4 5 7 6 8 10. find out the probability of picking an even number
    7·1 answer
  • What is the recursive formula for this arithmetic sequence -16,-7,2,11,
    5·1 answer
  • Three bacteria are ina dish. Each hour the number of bacteria increases by four. If at the end of the first hour there are 12 ba
    11·1 answer
  • For the points (5,4)and (7,8), find the distance between the points and find the
    10·1 answer
  • Describe how to write 6,397,000,000 in scientific notation.
    10·1 answer
  • Please help im being timed
    12·2 answers
  • If you are using algebra tiles to factor a trinomial of the form ax2 + bx + c, when would you need to bring in zero pairs? Why?
    8·2 answers
  • the king is having a sale where customers can buy 4 new tires for 419.96 what is the unit price of the tires
    8·1 answer
  • Which expressions are equivalent to g + h + (j + k)? Check all that apply.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!