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 the value of 5 to the power of 4 over 5 to the power of 6?
lubasha [3.4K]
If the question is 5^4 divided by 5^6 the asnwer is .04
7 0
2 years ago
Read 2 more answers
Bárbara come la tercera parte de una caja de bombones. Su papá luego compra 7 bombones más y los pone en la caja. ¿Cómo se repre
Maksim231197 [3]

Answer:

Bárbara come la tercera parte de una caja de bombones. Su papá luego compra 7 bombones más y los pone en la caja. ¿Cómo se representa la cantidad de bombones que hay ahora en la caja?

Step-by-step explanation:

3 0
2 years ago
Can the sides of a triangle have lengths 3.5, 10.9, and 14.4?
andrew11 [14]

Answer:

No

Step-by-step explanation:

A triangle can NOT have those lengths because any side of a triangle has to have a length greater than the sum of the other two sides. In this case, 14.4, one of the sides, is not greater than the sum of the other two sides (which is also 14.4).

Hope this helps :)

4 0
2 years ago
-2(8p+2)-3(2-7p)-2(4+2p)=0
zysi [14]

-2(8p+2)-3(2-7p)-2(4+2p)=0

mutiply the first bracket by -2

(-2)(8p)= -16p

(-2)(+2)= -4

mutiply the second bracket by -3

(-3)(2)= -6

(-3)(-7p)= 21p

mutiply the third bracket by -2

(-2)(4)= -8

(-2)(+2p)= -4p

-16p-4-6+21p-8-4p= 0

-16p+21p-4p-4-6-8= 0 ( combine like terms)

5p-4p-4-6-8= 0

p-4-6-8= 0

p-10-8= 0

p-18= 0

move -18 to the other side to get p by itself

sign changes from -18 to +18

p-18+18= 0+18

p= 0+18

Answer: p= 18

8 0
3 years ago
A recipe for 4 batches of bread uses 5 cups of flour. Harun wants to know how many cups of flour are needed for 1 batch. Judith
Viktor [21]

Answer: 8/10 of a cup

I am unsure of the 2nd half of the question

Step-by-step explanation: If you divide 5 by 4 then you will get the amount of cups of flour are needed for 1 batch

8 0
3 years ago
Read 2 more answers
Other questions:
  • The Logan Company issued 140 shares of its $12 par value stock for $14 per share. The entry to record the receipt of cash and is
    10·1 answer
  • actually post 17 status updates on her Facebook wall each day. Roberto posts 21 status updates on his Facebook wall each day. Pa
    10·1 answer
  • As of mid-2016, the world's population was about 7.4 billion people. The population of the United States was 324 million.
    9·1 answer
  • The equation of the graphed line is x + 2y = 5. What is the x-intercept of the graph?
    13·2 answers
  • What is the unit rate for 360 miles in 6 hours
    12·1 answer
  • I need help with this question please<br> ASAP!!!!!!!!!
    14·1 answer
  • What is the volume of the rectangular prism​
    14·2 answers
  • Convert the fraction 1/(x+1) to a denominator of x*3 + 1
    10·1 answer
  • I need help please?!!!!
    6·1 answer
  • PLEASE HELP ME !!!!!!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!