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
AleksandrR [38]
3 years ago
9

Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the -score for each of the five observations (to 2 decimal

s). Enter negative values as negative numbers. Observed value -score
Mathematics
1 answer:
dybincka [34]3 years ago
4 0

Answer:

Hence, the score for each of the five observations are -1.25,1.25,-0.75,0.50,0.25

Given :

Sample with data values of x_i  10,20,12,17 and 16

Sample sizen=5

To find:

Compute the score for each of the five observations.

Explanation :

\because Sample mean \bar{x}=\frac{\sum x_i}{n}

                     \Rightarrow \bar{x}=\frac{10+20+12+17+16}{5}=\frac{75}{5}

                    \Rightarrow \bar{x}=15

Standard deviation \sigma=\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1}}

                             \Rightarrow \sigma=\sqrt{\frac{(10-15)^2+(20-15)^2+(12-15)^2+(17-15)^2+(16-15)^2}{5-1}}

                            \Rightarrow \sigma=\sqrt{\frac{(-5)^2+(5)^2+(-3)^2+(2)^2+(1)^2}{4}}

                           \Rightarrow \sigma=\sqrt{\frac{25+25+9+4+1}{4}}

                          \Rightarrow \sigma=\sqrt{\frac{64}{4}} =\sqrt{16}

                         \Rightarrow \sigma=4

\because The score of the observations Z is \frac{x-\bar{x}}{\sigma}.

So, when (x=10),       Z=\frac{10-15}{4}=-1.25

     when (x=20),       Z=\frac{20-15}{4}=1.25

     when (x=12),      Z=\frac{12-15}{4}=-0.75

    when  (x=17},       Z=\frac{17-15}{4}=0.50

    when (x=16)       Z=\frac{16-15}{4}=0.25

You might be interested in
A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. ​(a) Describe the
Ivanshal [37]

Answer:

a) \bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})

With:

\mu_{\bar X}= 83

\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3

b) z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2

P(Z>2) = 1-P(Z

c) z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45

P(Z

d) z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1

z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2

P(-1.2

Step-by-step explanation:

For this case we know the following propoertis for the random variable X

\mu = 83, \sigma = 27

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})

With:

\mu_{\bar X}= 83

\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3

Part b

We want this probability:

P(\bar X>89)

We can use the z score formula given by:

z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And if we find the z score for 89 we got:

z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2

P(Z>2) = 1-P(Z

Part c

P(\bar X

We can use the z score formula given by:

z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And if we find the z score for 75.65 we got:

z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45

P(Z

Part d

We want this probability:

P(79.4 < \bar X < 89.3)

We find the z scores:

z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1

z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2

P(-1.2

8 0
3 years ago
Can you plz help me i need it
Snowcat [4.5K]

Answer:

v= -2

Step-by-step explanation:

2v + 7 = 3

(-7 both sides)

2v = -4

(divide bu 2 on both sides)

v = -2

hope this helps!!!!!  :)

3 0
3 years ago
Which equation represents a parabola that has a focus of (0 0) and a directrix of y = 2
Ilya [14]
The answer is 3 because z to the y a-1
3 0
3 years ago
Read 2 more answers
Which is bigger 8 or -3
NikAS [45]

8 is the greatest

Note the sign, and look at it on a number line.

8 is bigger than -3 by 11

hope this helps

4 0
3 years ago
Read 2 more answers
What is the maximum percentage of net spendable income that should be set aside for transportation?
pychu [463]
A. 15% the maximum percentage of the spendable income that should be set aside for transportation is 15%.
4 0
3 years ago
Read 2 more answers
Other questions:
  • How many ways can you write the ratio 7:20 as a fraction without zeros at the end?
    13·1 answer
  • A boy is building a pyramid out of building blocks. He puts 20 blocks in the first row, then he puts 19 blocks in the row above,
    14·1 answer
  • What is the slope of the line that cuts through the points (1, -5) and (3, 5)
    15·1 answer
  • Fourteen seniors were asked how many minutes they spent on doing their homework the previous night. The data is displayed below.
    14·2 answers
  • Find the measure of the numbered angles
    6·2 answers
  • WILL MARK YOU BRAINLIEST
    15·1 answer
  • Which has more power: odds or evens? Why?
    12·2 answers
  • On a coordinate plane, what is the distance between the points (-1,5) and (2,5)? Enter the answer in the box.
    10·1 answer
  • Use the definition of the derivative to differentiate v=4/2 pie r^3
    7·1 answer
  • You have a pet hamster and a pet mouse. The hamster weighs 416 of a pound. The mouse weighs 116 of a pound. How much more does t
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!