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
Bingel [31]
3 years ago
7

In the journal Knowledge Quest (January/February 2002), education professors at the University of Southern California investigat

ed children's attitudes toward reading. One study measured third through sixth graders' attitudes toward recreational reading on a 140-point scale (where higher scores indicate a more positive attitude). The mean score for this population of children was 106 points, with a standard deviation of 16.4 points. Consider a random sample of 36 children from this population, and let x represent the mean recreational reading attitude score for the sample.
(Give answers to 4 decimal places.)

a) What is ?x?

b) What is ?x?

c) What sample mean would be the cutoff for the bottom 10% of sample means. (You are being asked for the 10th percentile of sample means.)

d) Find P(x < 100).
Mathematics
1 answer:
Greeley [361]3 years ago
6 0

Answer:

a,b) x represents the general attitude of these students toward recreational reading.

c) The 10th percentile of sample means is 102.51.

d) P(x < 100) = 0.01390

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by

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

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 pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this case, we have that:

The mean score for this population of children was 106 points, with a standard deviation of 16.4 points, so \mu = 106, \sigma = 16.4.

a,b) What is x?

x represent the mean recreational reading attitude score for the sample. So x represents the general attitude of these students toward recreational reading.

c) What sample mean would be the cutoff for the bottom 10% of sample means. (You are being asked for the 10th percentile of sample means.)

This is the value of X when Z has a pvalue of 0.10.

Looking at the Z table, that is Z = -1.28.

We are working with the mean of the sample, so we have to find the standard deviation of the sample. That is

s = \frac{\sigma}{\sqrt{n}} = \frac{16.4}{\sqrt{36}} = 2.73

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

-1.28 = \frac{X - 106}{2.73}

X - 106 = -1.28*2.73

X = 102.51

The 10th percentile of sample means is 102.51.

d) Find P(x < 100).

This is the pvalue of Z when X = 100.

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

Z = \frac{100 - 106}{2.73}

Z = -2.20

Z = -2.20 has a pvalue of 0.01390.

So P(x < 100) = 0.01390.

You might be interested in
What is the correct way to divide 1.6/6.4
Alex777 [14]
You would do 6.4/1.6 because big should come first or the number will change
8 0
3 years ago
Four times the sum of a number and 15 is at least 120. Let x represent the number. Find all possible values for x.
Aleksandr [31]
4(x + 15) > = 120
4x + 60 > = 120
4x > = 120 - 60
4x > = 60
x > = 60/4
x > = 15...........so ur answer is 15 or more
4 0
3 years ago
HELP ASAP WILL GIVE BRAINLIEST PLEASE
Vlad1618 [11]

Answer is B  Mr James


Lets convert all the fractions, percentages to decimals:_

Mr James:  5/8 = 0.625

Miss Smith: 0.61

Mrs Lawson: 9/16 = 0.5625

Mr Tosh: 0.58

Mrs Cagle 0.53

So Mr James corrected the most homework.




8 0
3 years ago
Read 2 more answers
Step 1: 5 = negative 2 (negative StartFraction 3 Over 10 EndFraction) + b. Step 2: 5 = StartFraction 6 Over 10 EndFraction + b.
defon

Answer:

D.) Step 6: student needed to add the b value.

Step-by-step explanation:

I got it wrong and it gave me the right answer, which is what i provided, D.

4 0
3 years ago
Read 2 more answers
Rachel rounded 16,473 to the nearest hundred.Then she rounded her anzer to the nearest thousand.What is the final number
musickatia [10]

The hundreds place is underlined: 16,<u>4</u>73.

Look at the number to the right of the hundreds place. It is a 7. Because 7 is greater than 5, round up

16473 rounded to the nearest hundred is 16500

Next, she takes the number to round to the nearest thousand.

Remember that 5 and greater round up.

16500 rounded to the nearest thousand is 17000

17000 is your answer

hope this helps

8 0
3 years ago
Other questions:
  • the area of a rectangle is144j^9k^15 square units. if the width of the rectangle is 8j^4k^5 units, what is the rectangle lingth​
    11·1 answer
  • Hi can someone help me out with this quickly?
    11·1 answer
  • A team of 4 people participated in a 400 yard relay race. Each team member runs the same distance. The team complete the race in
    12·1 answer
  • How do I graph y+x= -3
    12·1 answer
  • 3(6x - 4) = 22x
    13·1 answer
  • If a dog weighs 240 ounces, how many grams does the dog weigh?
    9·1 answer
  • Need some help here... Image below. Please try and explain how you get the answer, as I do want to try and learn the material.
    14·2 answers
  • After restocking the vending machines, Efrain determined that 2 out of every 5 packages of candy sold were M&amp;M'S®. The vendi
    14·2 answers
  • HEJEKEKFLSKSLCBDMLDgbnnbvgfknfnfkskskfjgjdkwkdjdkdkdkdjdks
    9·2 answers
  • Jed wants to prove that his test scores are greatly improving. He makes the graph shown here.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!