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
I need help what is 7h+1−h+4?
zloy xaker [14]

Answer:

6h+5

Step-by-step explanation:

7h-h=6h

1+4=5

Hope this helps :)

3 0
3 years ago
Read 2 more answers
Hey pls help worth 30 points
GrogVix [38]

Step 1: Find the slope:

    m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{10-6}{6-5} = \dfrac{4}{1} = 4

Step 2: Set up your equation y-y_1=m(x-x_1) using one of the points.

    Using (5,6) we have y-6 = 4(x-5).

    Using (6,10) we have y-10 = 4(x-6)

Both of those equations would be correct.

5 0
3 years ago
Read 2 more answers
I REALLY NEED HELP PLEASE
Nezavi [6.7K]

Answer:

10

Step-by-step explanation:

given

\frac{s + ( - 7)}{ - 1}

we first need to simplify the expression before we find it's value when s=-3

positive times negative=negative

so the equation becomes

\frac{s - 7}{ - 1}

substituting s=-3 into the equation.

\frac{ - 3 - 7}{ - 1}

=

\frac{ - 10}{ - 1}

=the negatives cancel out leaving

= 10

7 0
3 years ago
Answer the following question CORRECTLY I will know if this is wrong. I WILL REPORT ANY INCORRECT ANSWERS!
vredina [299]

Answer is: B) An allowable amount of variation of a specified quantity, especially in the dimensions of a machine part.

Tolerance is how much something can take.

5 0
3 years ago
Read 2 more answers
,/,/,/,//,/,/,/,//,,,,,,///,,/,///,/,,/,,/,/,/,/,,
vladimir2022 [97]

Answer :

hmmm ... :0 ?

3 0
2 years ago
Read 2 more answers
Other questions:
  • There are 34 students in J2.
    13·1 answer
  • Gloria’s mother is 2.5 times as old as Gloria. Gloria is 16 how old is her mother
    10·1 answer
  • Tanya has a bond with a 5.9 yield, a big price of $1950, and a face value of $2000. what is the original coupon rate of this bon
    7·2 answers
  • Malik borrowed $105 from his brother and plans to repay $12 per week. He creates a table to help him determine the
    8·1 answer
  • Is the following relation a function?<br> Yes or no
    6·1 answer
  • Can someone answer this question?
    15·2 answers
  • Use the distributive property to rewrite each expression in it's equivalent form 9a-3/3 ,Just 3 please
    9·1 answer
  • Someone pls help me.
    14·1 answer
  • EZ 15 points!
    10·1 answer
  • When you round a number, which digit in the number helps you decide to round up or down?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!