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
SashulF [63]
3 years ago
7

In a population distribution, a score of x=57 corresponds to z=-0.25 and a score of x=87 corresponds to z=1.25. Find the mean an

d standard deviation for the population.
Mathematics
2 answers:
Eva8 [605]3 years ago
7 0

Answer: The mean is 62 and the standard deviation is 20 for the population.

Step-by-step explanation:

Let \mu be the mean and \sigma be the standard deviation .

Formula to calculate z-score corresponds to random variable x on normal curve.

Z=\dfrac{X-\mu}{\sigma},  

Given : In a population distribution, a score of x=57 corresponds to z=-0.25 and a score of x=87 corresponds to z=1.25.

-0.25=\dfrac{57-\mu}{\sigma}\\\\-0.25\sigma=57-\mu---------(1)

1.25=\dfrac{87-\mu}{\sigma}\\\\1.25\sigma=87-\mu----------(2)

Eliminate equation(1) from equation(2), we get

1.50\sigma=30\\\\\Rightarrow\ \sigma=\dfrac{30}{1.5}=20

Put value of \sigma=20 in (1)

1.25(20)=87-\mu\\\\87-\mu=25,\\\\\Rightarrow\mu=87-25=62.

Hence, the mean is 62 and the standard deviation is 20 for the population.

Serggg [28]3 years ago
3 0

Here is dependence between scores and x-values:

Z_i=\dfrac{X_i-\mu}{\sigma},

where \mu is the mean, \sigma is standard deviation and i changes from 1 to 2.

1. When i=1, Z_1=-0.25,\ X_1=57, then

-0.25=\dfrac{57-\mu}{\sigma}.

2. When i=2, Z_2=1.25,\ X_2=87, then

1.25=\dfrac{87-\mu}{\sigma}.

Now solve the system of equations:

\left\{\begin{array}{l}-0.25=\dfrac{57-\mu}{\sigma}\\ \\1.25=\dfrac{87-\mu}{\sigma}.\end{array}\right.

\left\{\begin{array}{l}-0.25\sigma=57-\mu\\ \\1.25\sigma=87-\mu.\end{array}\right.

Subtract first equation from the second:

1.25\sigma-(-0.25\sigma)=87-57,\\ \\1.5\sigma=30,\\ \\\sigma=20.

Then

1.25=\dfrac{87-\mu}{20},\\ \\87-\mu=25,\\ \\\mu=87-25=62.

Answer: the mean is 62, the standard deviation is 20.

You might be interested in
The floor of a rectangular room is 300 cm long and 180 cm wide. to carpet the floor? How many small tiles are needed​
Vinvika [58]

The number of small tiles are needed​ is 300 tiles.

<h3>Number of tiles needed</h3>

Using area of rectangular formula

Area of the room = length(l) × breadth (b)

Area of the room=300 cm×180 cm

Area of the room=54,000 cm²

Number of tiles needed = Area of rectangular region / Area of one tile

Number of tiles needed=54,000/180

Number of tiles needed=300 tiles

Therefore the number of small tiles are needed​ is 300 tiles.

Learn more about number of tiles needed here:brainly.com/question/2136390

#SPJ1

4 0
2 years ago
Scott and Ariel want to make as much as snack mix as possible, but no more than 25 cups of mix. I they can use only full cups of
photoshop1234 [79]

Answer:

hello your question has some missing parts attached below is the missing information

answer : Scott will make 5 snack mix without going over

Step-by-step explanation:

Given that:

Scott makes a snack  mix with ; 2 cups of Almonds and 3 cups of raisins

=  5cups per snacks mix

Ariel makes a snack mix with : 3 cups of almonds and 5 cups of sunflower seeds = 8 cups per snack mix

<u>Now back to your question above</u>

Given that : No more than 25  full cups is required to make a snack mix

For Scott

= 25 / 5 = 5 snack mix ( No make overs )

For Ariel

= 25 / 8 = 3.125 snack mix ( there is a makeover of 0.125 )

Hence it can be said that Scott will make the most mix without going over

8 0
3 years ago
HELP WILL GIVE BRAINLyEST AND CASHH APP 10$USD
laiz [17]

1. Idc about cash, pls don't send me any, virtual goals (brainly points/brainliest) are enough.

Answer:

B.

Step-by-step explanation:

It is definitely not C. or D., so we already have narrowed down the choices.

And A. has Julie older than Paula so it isn't A either, so it has to be B.

7 0
3 years ago
Read 2 more answers
What does the letter c stand for in the formula a2 +b=c??
Travka [436]

Answer:

The answer is C

3 0
3 years ago
Hey can anybody help me out
NikAS [45]
You should be able to find the answer try using the tiger math app
6 0
3 years ago
Other questions:
  • FIRST RIGHT ANSWER GETS BRAINLLEST If you spin the spinner below 20 times, which of the following outcomes are reasonable? Selec
    6·2 answers
  • Q and r are independent events. if p(q) = 1/4 and p(r)=1/5, find p(q and r)
    11·1 answer
  • Jan ran a mile in 0.14 hours. Convert the hours into a fraction. hours
    13·2 answers
  • Jane sent 96 texts last week. She sent 52 texts to her friend Jeff. She sent 28 texts to her friend Megan. What is the ratio of
    13·2 answers
  • Find the angular speed w for each of the following.<br>33. the hour hand of a clock<br>​
    10·1 answer
  • Dennis grilled 10 burgers and 25 hot dogs for
    10·2 answers
  • It took Everly 55 minutes to run a 10-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minu
    9·1 answer
  • Help me please!! The next model of a sports car will cost 12.2% less than the current model. The current model costs $34,000. Ho
    13·1 answer
  • Nicholas has $50 to use while he is on a vacation. He decides to spend $5
    15·1 answer
  • Last week, Riley worked 7.5 hours per day for 3 days and earned a total of $306.45.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!