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
goldfiish [28.3K]
3 years ago
9

g The average midterm score of students in a certain course is 70 points. From the past experience it is known that the midterm

scores in this course are Normally distributed. If 29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points, find the probability that the average midterm score of these students is at most 75 points. (Round your final answer to 3 places after the decimal point).
Mathematics
1 answer:
spayn [35]3 years ago
8 0

Answer:

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average midterm score of students in a certain course is 70 points.

This means that \mu = 70

29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.

This means that \sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44

Find the probability that the average midterm score of these students is at most 75 points.

This is the pvalue of Z when X = 75. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{75 - 70}{2.44}

Z = 2.05

Z = 2.05 has a pvalue of 0.98.

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

You might be interested in
What is 6/7 Answer quickly please!!
nevsk [136]

Answer: 0.8

Step-by-step explanation:

6 0
3 years ago
In 1995, Orlando, Florida, was about 175,000. At the time, the population was growing at a rate of about 2000 per year. Write an
gladu [14]

Answer:

y= 2000 * x + 175000

Step-by-step explanation:

Given is Population is 175,000

Increase in rate = 2000/year

Let x be the population in 1995 which is C= 175,000

y= Population after per year

We know the formula for slope intercept form is

y= mx + C     ............... (i)

Now from the suppose values and given

m= 2000

Now putting values in equation (i) gives

y= 2000 * x + 175000

Here x is the No of years

6 0
3 years ago
Convert 6.7 minutes to seconds.
Diano4ka-milaya [45]

Answer:

402 seconds

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Solve the following:<br> A) 4x-1/2=x+7<br> B) 3x+2=2x+13/3<br> C) 2x-7/4=3+x/3
s2008m [1.1K]

Answer:

a. 2.5  

b. 2.333

c. 2.85

Step-by-step explanation:

A) 1. subtract -x on both sides              2. to get 3x-1/2=7  

3. Add 1/2 on both sides                    4. to get 3x=7.5    

5. divide 3 on both sides                   6. To get... x=2.5

B)1. Same process.                               2. x+2=13/3        

3. x=13/3-2                                         4. x= 2.33(repeating)

C) 1. same process.                           2. 2x-x/3=3+7/4

3. 2x-x/3=4.75                                  4. Isolate -x/3  

5.-x/3=4.75-2x                                    6. multiply both sides by 3          

7. -x=14.25-6x                                      8. 5x=14.25

9. x= 2.85

* remember to distribute the 3 to each variable.

4 0
3 years ago
What type(s) of symmetry does the figure have?
Troyanec [42]

Answer:

both points and rotational only

4 0
3 years ago
Read 2 more answers
Other questions:
  • Which graph represents the solution to the given system? (1 point) <br> Y=-3x+4 and y=2x-1
    15·1 answer
  • A line is parallel to y= 1/2x +6 and passes through (–8, 0). What is the equation of the line?
    9·2 answers
  • Helene wrote a report. It took her 4 hours to write 24 pages.
    5·1 answer
  • 3(v + 2) + 4 = 13<br> HELP ME!!
    15·2 answers
  • Mike is working on solving the exponential equation 37x = 12; however, he is not quite sure where to start. Using complete sente
    7·2 answers
  • What is the maximum possible value of this number 18.6
    11·2 answers
  • 8. How many ounces of liquid are in 4 gallons
    10·2 answers
  • I need help with this homework I have a deadline
    13·1 answer
  • nathan smiled at 50 people one day and recorded that 36 people smiled back at him.Based on his observations how many people shou
    6·1 answer
  • Please help me answer the question in the image
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!