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
soldier1979 [14.2K]
2 years ago
14

The distribution of SAT II Math scores is approximately normal with mean 660 and standard deviation 90. The probability that 100

randomly selected students will have a mean SAT II Math score greater than 670 is approximately what
Mathematics
1 answer:
gayaneshka [121]2 years ago
7 0

Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

<h3>Normal Probability Distribution</h3>

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

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of 660, hence \mu = 660.
  • The standard deviation is of 90, hence \sigma = 90.
  • A sample of 100 is taken, hence n = 100, s = \frac{90}{\sqrt{100}} = 9.

The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:

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

By the Central Limit Theorem

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

Z = \frac{670 - 660}{9}

Z = 1.11

Z = 1.11 has a p-value of 0.8665.

1 - 0.8665 = 0.1335.

0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213

You might be interested in
A line that includes the point (4,3) has a slope of 8. What is its equation in point-slope form?
anzhelika [568]
............................................
3 0
2 years ago
Pleas help me with this answer https://brainly.com/question/19857050
mylen [45]
What ??????? !.9:9..jdkKzksoq
3 0
2 years ago
What is 80% as a fraction in reduced form?
Elza [17]

Answer:

45

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Dr. Blumen invested $5,000 part of it was invested in bonds at a rate of 6% in the rest was invested in a money market at the ra
abruzzese [7]
So... let's say the amounts invested were "a" at 6% and "b" at 7.5%.

ok.. hmm what's 6% of a? well, (6/100) * a or 0.06a.
what's 7.5% of b? well, (7.5/100) * b or 0.075b.

now... we know, whatever "a" and "b" are, they total the investment of 5000 bucks, thus a + b = 5000

and the interest yielded was 337.50, thus 0.06a + 0.075b = 337.50

thus    \bf \begin{cases}&#10;a+b=5000\implies \boxed{b}=5000-a\\&#10;0.06a+0.075b=337.50\\&#10;----------\\&#10;0.06a+0.075\left( \boxed{5000-a} \right)=337.50&#10;\end{cases}

solve for "a", to see how much was invested at 6%.

what about "b"?  well, b = 5000 - a.
6 0
3 years ago
Read 2 more answers
You want to rent movies online, The new service charges a sign up fee of $10, Then,
gavmur [86]

Answer:

y=12x+10 or f(x)=12x+10

Step-by-step explanation:

If it costs $12 per month to rent as many movies as you want, then that can be represented as 12x

Since $10 is a flat fee and doesn't change, this gets added seperately to 12x

Thus, the final equation is y=12x+10 or f(x)=12x+10

Hope this helped!

3 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone please help me
    7·2 answers
  • Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at
    5·2 answers
  • Solve the following inequality for dd. Write your answer in simplest form. −7d−3&gt;2d-10
    12·1 answer
  • Which is the best estimate for the quotient of 1,002.821 ÷ 0.499?
    9·2 answers
  • Janet walked 3.75 miles yesterday what is the word form of 3.75
    6·2 answers
  • You walk around a circle which has a diameter of 9 m, how far have you walked?
    7·2 answers
  • What do you know to be true about the values of p and q?
    8·2 answers
  • Is 2500 a perfect cube ?
    14·2 answers
  • If m = 34 and n = 5, what is the value of the following expression?
    11·2 answers
  • Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures televisions, can be m
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!