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
Vsevolod [243]
3 years ago
9

The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the sta

ndard deviation is 50. A subject earns a score of 155. How many standard deviations from the mean is the value 155
Mathematics
1 answer:
galina1969 [7]3 years ago
5 0

Answer:

The value <em>155</em> is zero standard deviations from the [population] mean, because \\ x = \mu, and therefore \\ z = 0.

Step-by-step explanation:

The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:

\\ z = \frac{x - \mu}{\sigma} [1]

Where

  • z is the <em>z-score</em>.
  • x is the <em>raw score</em>: an observation from the normally distributed data that we want <em>standardize</em> using [1].
  • \\ \mu is the <em>population mean</em>.
  • \\ \sigma is the <em>population standard deviation</em>.

Carefully looking at [1], we can interpret it as <em>the distance from the mean of a raw value in standard deviations units. </em>When the z-score is <em>negative </em>indicates that the raw score, <em>x</em>, is <em>below</em> the population mean, \\ \mu. Conversely, a <em>positive</em> z-score is telling us that <em>x</em> is <em>above</em> the population mean. A z-score is also fundamental when determining probabilities using the <em>standard normal distribution</em>.

For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], <em>one standard deviation above</em> from the population mean. A z-score = -1 is also one standard deviation from the mean but <em>below</em> it.

These standardized values have always the same probability in the <em>standard normal distribution</em>, and this is the advantage of using it for calculating probabilities for normally distributed data.

A subject earns a score of 155. How many standard deviations from the mean is the value 155?

From the question, we know that:

  • x = 155.
  • \\ \mu = 155.
  • \\ \sigma = 50.

Having into account all the previous information, we can say that the raw score, <em>x = 155</em>, is <u><em>zero standard deviations units from the mean.</em></u> <u><em>The subject   earned a score that equals the population mean.</em></u> Then, using [1]:

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

\\ z = \frac{155 - 155}{50}

\\ z = \frac{0}{50}

\\ z = 0

As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:  

\\ x = \mu

Therefore

\\ z = 0

So, the value 155 is zero standard deviations <em>from the [population] mean</em>.

You might be interested in
Carlton is using the following data samples to make a claim about the house values in his neighborhood:
olga2289 [7]
The answer is A because there is a outlier which is $100,000
8 0
3 years ago
Read 2 more answers
A car traveling 118 miles uses 4 gallons of gas. At this rate, how many miles can it travel using 13 gallons of gas
erastova [34]

Answer:

12 miles per gallon

Step-by-step explanation:

I hope this helps

3 0
3 years ago
Read 2 more answers
I will give Brainliest!!!
mixer [17]

Answer: C

Step-by-step explanation:

x = 2\sqrt{y+2} - 6

x + 6 = 2\sqrt{y+2}

((x+6)/2 = \sqrt{y+2} )^2

(x+6/2)^2 = y+2

y = (x+6/2)^2 -2

y= 1/4x^2 +3x +7

3 0
3 years ago
A regular square pyramid just fits inside a cube (the base of the pyramid is congruent to a face of the cube and
zlopas [31]
Volume of reg sq. pyramid = vp
vp = 1/3×s^2×h, where s = side and h = height
Volume of cone = vc =1/3×h×pi×r^2
Now we know that h is the same for both, and the cones diameter = s of square base, so radius (r) = 1/2 s
so now vc = 1/3×h×pi×(1/2s)^2
let's remove the same items for both vc and vp
so 1/3 and h
now let's plug an arbitrary number into each:
vc = pi (10/2)^2 = 3.14×25 = 78.54
vp = s^2 = 10^2 = 100
So any square pyramid has slightly more volume than the cone
4 0
2 years ago
Linnea is renting a bike. It costs $4.50 per hour plus a $5 deposit. a. Draw a line to show the relationship between the number
lana [24]

Answer:

(see image)

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • My math homwork is asking me for the word form and the expanded form for 3.4 and 2.51,and i don't understand this. we just start
    6·1 answer
  • Differentiate: f(x) = 3x ln(6x) − 3x
    7·1 answer
  • Expression for 10 divide into fifths from 20 divided in half
    9·1 answer
  • A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries wil
    10·1 answer
  • The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The le
    15·2 answers
  • Find the surface area of the figure.
    8·1 answer
  • Can anyone help with this? Would appreciate it!
    8·1 answer
  • WILL MARK YOU BRAINLIEST
    7·2 answers
  • What is the unit price for trail mix if a 8 ounce bag cost $2.80.
    15·1 answer
  • Ok here you go theyhatemeforlif3
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!