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
marysya [2.9K]
3 years ago
15

Polly's Polls asked 1850 second-year college students if they still had their original major. According to the colleges, 65% of

all second-year college students still had their original major. What is the probability that Polly's Polls' random sample will give a result within 1% of the true value? Assume the normal model applies here. You may use your calculator or reference the z-tables when working with normal models.
Mathematics
1 answer:
suter [353]3 years ago
4 0

Answer:

The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424

Step-by-step explanation:

The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.

Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.

The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.

We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words

W = \frac{X-\lambda}{\sigma} = \frac{X-1202.5}{20.5152}

The values of the cummulative function of the standard normal variable W, which we will denote \phi are tabulated and they can be found in the attached file.

Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.

P(1184 < X < 1221) = P(\frac{1184-1202.5}{20.5152} < \frac{X-1202.5}{20.5152} < \frac{1221-1202.5}{20.5152})\\ = P(-0.9018 < W < 0.9018) = \phi(0.9018) - \phi(-0.9018) = \phi(0.9018)-(1-\phi(0.9018))\\ = 2\phi(0.9018)-1 = 2*0.8212-1 = 0.6424

Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.

Download pdf
You might be interested in
A 24-ft ladder leans against the outside wall of a school, waiting for someone to climb and fix a broken window. The base of the
Aloiza [94]
I am learning this right now but in two hours I will tell you
6 0
2 years ago
Read 2 more answers
Mice and Pain Can you tell if a mouse is in pain by looking at its facial expression? A new study believes you can. The study1 c
kotykmax [81]

<u>Explanation:</u>

1. a) Null hypothesis: There is <em>no</em> statistically significant relationship between the mouse grimace scale and the amount of pain felt by mouse.

b) Alternate hypothesis: There is a statistically-significant relationship between the mouse grimace scale and the amount of pain felt by mouse.

2. Yes, because a statistically significant data implies that there is sufficient evidence to believe the study, based on the results of the findings.

3. No, since the variables are different in this case. Here we are dealing with a non-painful solution so there may be no sample correlation as extreme as that found in the original study.

4. Possibly, because every hypothesis is an assumption until it is proven. Thus, in every statistical research, there may be different findings.

3 0
3 years ago
HELP!<br> Find the Area of the triangle
Zigmanuir [339]

Answer:

A ≈ 65.8 m²

Step-by-step explanation:

Given 2 sides and the angle between them then the area (A) is

A = \frac{1}{2} bc sinA

   = 0.5 × 19.9 × 10.7 × sin38.17°

   ≈ 65.8 m² ( to 1 dec. place )

6 0
2 years ago
215% of 41.8 is what number
salantis [7]
Ith Calculator

41.8 = 100%
215%/100% = 2.15
41.8 x 2.15 = 89.87

Without Calculator

41.8 = 100%

x2
83.6 = 200%

/10
4.18 = 10%

/20 
2.09 = 5%

200 + 10 + 5 = 215%
83.6 + 4.18 +2.09 = <span>89.87</span>
4 0
2 years ago
Read 2 more answers
What is the sum of the first 39 positive odd numbers?
liq [111]
1-39 ODD:
1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39
Now you'd add them all up.
1+3+5+7+9 = 25
11+13+15+17+19 = 75
21+23+25+27+29 = 125
31+33+35+37+39 = 175
Add the totals:
25+75+125+175
The answer would be 400.
7 0
3 years ago
Other questions:
  • Of these integers, -65, -42, 65, and 90, which two are farthest apart on the number line?
    13·2 answers
  • The trash can is in the shape of a cylinder that has a radius of 2 ft and a height of 5 feet what is the volume of the trash can
    13·2 answers
  • A video game costs $29.35 at one store and $32.79 at another store. Generate two equivalent expressions and then find how much m
    12·1 answer
  • 243.875 to the nearest ten
    14·2 answers
  • What is 4.35 rounded to the nearest hundred
    13·1 answer
  • The probability that a student has a Visa card (event V) is .63. The probability that a student has a MasterCard (event M) is .1
    11·1 answer
  • Sine divided by Cosine is equal to Tangent. True or false?
    7·1 answer
  • Johan's family took him out to dinner to celebrate his amazing 2nd
    12·1 answer
  • ANYONE PLEASE HELP ME IN MY MATH HOMEWORK I REALLY NEED THE ANSWER RIGHT NOW BECAUSE I HAVE TO PASS THIS TOMORROW:(
    13·1 answer
  • Identify the x and y intercepts and write as an ordered pair 1. 3. 5. 2. 6.​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!