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
Alex Ar [27]
3 years ago
9

To help students improve their reading, a school district decides to implement a reading program. It is to be administered to th

e bottom 15% of the students in the district, based on the scores on a reading achievement exam given in the child's dominant language. The reading-score for the pooled students in the district is approximately normally distributed with a mean of 122 points, and standard deviation of 18 points. a. Find the probability of students score above 140 points? b. What is the 15th percentile of the students eligible for the program?
Mathematics
1 answer:
Crank3 years ago
4 0

Answer:

a) P(X>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140-122}{18})=P(Z>1)

And we can find this probability using the complement rule and the normal standard table or excel and we got:

P(Z>1)=1-P(Z

b) z=-1.036

And if we solve for a we got

a=122 -1.036*18=103.35

So the value of height that separates the bottom 15% of data from the top 85% is 103.35.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(122,18)  

Where \mu=122 and \sigma=18

We are interested on this probability

P(X>140)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140-122}{18})=P(Z>1)

And we can find this probability using the complement rule and the normal standard table or excel and we got:

P(Z>1)=1-P(Z

Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X   (a)

P(X>a)=0.85   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.15 of the area on the left and 0.85 of the area on the right it's z=-1.036. On this case P(Z<-1.036)=0.15 and P(z>-1.036)=0.85

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-1.036

And if we solve for a we got

a=122 -1.036*18=103.35

So the value of height that separates the bottom 15% of data from the top 85% is 103.35.  

You might be interested in
Twice the sum of x and 6 is at most 52. What is the greatest value of x that satisfies the inequality that represents this situa
Shalnov [3]
Our inequality looks like this:
2(x+6)≤52
Using the Distributive Property, we have
2*x + 2*6 ≤52
2x+12≤52
Cancel the 12 by subtracting from both sides:
2x+12-12≤52-12
2x≤40
Divide both sides by 2:
2x/2 ≤ 40/2
x≤20
x cannot be any more than 20 to satisfy this inequality.
6 0
2 years ago
Read 2 more answers
if the hypotenuse of a special triangle of 45 45 90 was 10 radical 6 how would u solve for the hypotenuse
Vinvika [58]
Just do it it’s quite easy
3 0
3 years ago
Which of the following statements is false?
Sonja [21]
The second one is incorrect
4 0
3 years ago
Read 2 more answers
3. At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount,
Inessa [10]
(a) 3x=4(x-2.25) (or simplified: 3x=4x-9)

(b) 3x=4x-9
0=x-9
x=$9

(c) 3x9=27
4x9=36
36-9=27
and 27=27 therefore they spent the same and it is correct

(d) Tanya's items cost $9 each and Tony's items cost $2.25 less than this, or $6.75
3 0
3 years ago
What is slope of BE/ slope of AE in simplest form?
saul85 [17]

Answer:

Basically, you calculate your ratio and find what its is, but after that, you have to simplify it, giving you 4.


Step-by-step explanation:


3 0
3 years ago
Read 2 more answers
Other questions:
  • How to find x in a plane
    12·1 answer
  • 9 apples there are 6 fewer apples than oranges
    6·1 answer
  • According to a survey on us population, the probability that a man will live seventy-five years is 0.62 and that he will live up
    8·1 answer
  • Find all zeros of ƒ(x) = x^3 + 2x^2 – x – 2. Then determine the multiplicity at each zero. State whether the graph will touch or
    12·1 answer
  • A college raises its tuition in each of three consecutive years. If the percent increase by 5%, 9%, and 7%, determine the overal
    9·1 answer
  • What is 2/3 of 17? Do you need to find the greatest denominator?
    5·1 answer
  • your gas bill went up from $125 per month to $150 per month. what is the percent increase of your gas bill?
    10·2 answers
  • For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that
    9·1 answer
  • PLZ HELP<br> ANSWER BOTH QUESTIONS<br> THE SECOND ONE IS MORE OR LESS
    6·2 answers
  • Find the answer in simplest form.<br> 3 1/8 * 1 4/5=
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!