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
aliya0001 [1]
2 years ago
15

A certain standardized test's math scores have a bell-shaped distribution with a mean of 525 and a standard deviation of 119. Co

mplete parts (a) through (c)
(a) What percentage of standardized test scores is between 406 and 644?
(Round to one decimal place as needed.)
(b) What percentage of standardized test scores is less than 406 or greater than 644?
(Round to one decimal place as needed.)
(c) What percentage of standardized test scores is greater than 763?
Round to one decimal place as needed.)
Mathematics
1 answer:
joja [24]2 years ago
4 0

Using the normal distribution, it is found that:

a) 68.2% of standardized test scores are between 406 and 644.

b) 31.8% of standardized test scores are less than 406 or greater than 644.

c) 2.3% of standardized test scores are greater than 763.

<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.

In this problem:

  • The mean is of 525, hence \mu = 525.
  • The standard deviation is of 119, hence \sigma = 119.

Item a:

The proportion is the <u>p-value of Z when X = 644 subtracted by the p-value of Z when X = 406</u>, hence:

X = 644:

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

Z = \frac{644 - 525}{119}

Z = 1

Z = 1 has a p-value of 0.841.

X = 406:

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

Z = \frac{406 - 525}{119}

Z = -1

Z = -1 has a p-value of 0.159.

0.841 - 0.159 = 0.682.

0.682 = 68.2% of standardized test scores are between 406 and 644.

Item b:

Complementary event to the one found in item A, hence:

1 - 0.682 = 0.318.

0.318 = 31.8% of standardized test scores are less than 406 or greater than 644.

Item c:

The proportion is <u>1 subtracted by the p-value of Z when X = 763</u>, hence:

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

Z = \frac{763 - 525}{119}

Z = 2

Z = 2 has a p-value of 0.977.

1 - 0.977 = 0.023

0.023 = 2.3% of standardized test scores are greater than 763.

You can learn more about the normal distribution at brainly.com/question/24663213

You might be interested in
What is the place value of the number 9 in 328.095?
brilliants [131]

Answer:

The tenths place

6 0
3 years ago
Read 2 more answers
Which of the following will most likely produce sample proportions that are
masha68 [24]
The answer you are looking for is 14.
7 0
3 years ago
In April 2008, an audio CD was available for $14.01. the list price (full price) of the CD was $19.32. What was the percent disc
8_murik_8 [283]
19.30 - ( p / 100 )*19.32 = 14.01 ;
19.30( 1 - p/100 ) = 14.01 ;
1 - p/100 = 14.01 / 19.30
1 - p / 100 = 0.72 ;
p/100 = 1 - 72 / 100 ;
p/100 = 28 / 100 ;
p = 28 ;
The percent discount is 28% ;
4 0
3 years ago
9: Part A The diameter of a circle is 63 centimeters. ​Find its circumference. ​Use π=3.14. ​ A 31.5 centimeters B 98.91 centime
BaLLatris [955]
Part A:
The circumference of the circle is 197.92.

Explanation:
The formula for circumference of a circle is C=2 πr. If you insert the numbers, it would be C=2 x 3.14 x 31.5. Hence, the answer is 197.92.

Part B:
The area is 3117.25 square cm.

Explanation:
The formula for area of a circle is A= πr ². Inserting the numbers, it is A=3.14 x 31.5 ². Therefore the answer is 3117.25 cm ².
6 0
3 years ago
The number of blueberry muffins that a baker makes each day is
zysi [14]

Answer:

72 I think

Correct me if I'm wrong

6 0
3 years ago
Other questions:
  • Log squared 32 = y<br><br> find value of y
    12·1 answer
  • Sherita's club is selling grapefruit to raise money. For every box they sell, they get $1.35 profit. They have sold 84 boxes alr
    6·1 answer
  • A florist has 72 red roses and 40 white roses. If the florist creates the greatest number of identical bouquets possible with a
    12·1 answer
  • 1.
    15·2 answers
  • 1/100000 as a power of 10
    13·1 answer
  • #6 please help!<br> i will mark brainliest!
    8·2 answers
  • What is the answer for this one 4x + 16 = ?
    9·1 answer
  • Pls help no links pls
    13·2 answers
  • 83, 15, 50, 28, 52, 96 - What is the mean? What is the mode? What is the median?
    14·2 answers
  • The concentration of a drug in an organ at any time t (in seconds) is given by
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!