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
eimsori [14]
3 years ago
7

2. MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of

75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500.
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
7 0

Answer:

a) Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(75,15)  

Where \mu=75 and \sigma=25

The distribution for the sample mean \bar X is given by:

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

b) \mu represent the true average for the scores of the aptitude test

c) We can calculate the z scores and we got:

z = \frac{70.14-75}{\frac{15}{\sqrt{25}}}= -1.62

z = \frac{82.14-75}{\frac{15}{\sqrt{25}}}= 2.38

And we can calculate the probability with this difference:

P(-1.62

d) We can calculate the z scores and we got:

z = \frac{82.68-75}{\frac{15}{\sqrt{25}}}= 2.56

And we can calculate the probability with this difference:

P(Z

e) We can calculate the z scores and we got:

z = \frac{78.69-75}{\frac{15}{\sqrt{25}}}= 1.23

And we can calculate the probability with this difference:

P(Z

Step-by-step explanation:

a. What are the expected value, the standard deviation, and the shape of the sampling distribution of \bar X?

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(75,15)  

Where \mu=75 and \sigma=25

The distribution for the sample mean \bar X is given by:

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

b. What is the random variable in this problem? Define it in words.

\mu represent the true average for the scores of the aptitude test

c. What is the probability that the average aptitude test score in the sample will be between 70.14 and 82.14?

We can calculate the z scores and we got:

z = \frac{70.14-75}{\frac{15}{\sqrt{25}}}= -1.62

z = \frac{82.14-75}{\frac{15}{\sqrt{25}}}= 2.38

And we can calculate the probability with this difference:

P(-1.62

d. What is the probability that the average aptitude test score in the sample will be greater than 82.68?

We can calculate the z scores and we got:

z = \frac{82.68-75}{\frac{15}{\sqrt{25}}}= 2.56

And we can calculate the probability with this difference:

P(Z

e. What is the probability that the average aptitude test score in the sample will be less than 78.69?

We can calculate the z scores and we got:

z = \frac{78.69-75}{\frac{15}{\sqrt{25}}}= 1.23

And we can calculate the probability with this difference:

P(Z

You might be interested in
Write an equation of the line passing through the given point (6,-7) and having the given slope m=-9. Write the final answer in
Ede4ka [16]
Y-(-7)=-9(x-6)
Y+7= -9x+54
Subtract 7 from both sides
Y= -9x+47
3 0
3 years ago
Is (-3, -9) a solution of the equation y = 3x ?
makkiz [27]

Answer:

Yes.

Step-by-step explanation:

-3 * 3 = -9

3 0
3 years ago
What is the total area of each garden bed has a length of 4 feet Amelia
trasher [3.6K]
64 feet squared because 4 cubes
5 1
3 years ago
Read 2 more answers
PLEASE HELP MEE
KATRIN_1 [288]

Answer:

I'm only going to find the value of each variable

Step-by-step explanation:

V,Z,W,Y=39

X=94

Sorry, I didn't know how to explain the relevant angle relationships. '-' :(

8 0
3 years ago
N/5 + -6 = 9 <br> What is n ?
Tatiana [17]
Answer: 75

work: n/5 + -6 = 9
n/5 = 9+ 6
n/5 = 15
n = 15 x 5
n= 75
4 0
3 years ago
Other questions:
  • Can someone help me find the area..?
    7·2 answers
  • 3n-5=-8(6+5n) please solve this linear equation i need help
    13·2 answers
  • Find two consecutive whole numbers that square root113 lies between.
    5·1 answer
  • Help need to divide the fraction ​
    12·1 answer
  • Pattern is 3,-6,12,4,20
    9·1 answer
  • What are three different whole numbers whose sum and product are the same
    15·1 answer
  • Simplify 8.7+(1.5)2+4(3.5+6.2)0-3.1-1.5
    7·1 answer
  • Scores on a national math test are Normally distributed, with a mean score of 490 and a standard deviation of 50. Which test sco
    15·2 answers
  • What the answer please
    6·1 answer
  • Solve the following
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!