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
ollegr [7]
3 years ago
10

A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. ​(a) Describe the

sampling distribution of x overbar. ​(b) What is Upper P (x overbar greater than 89 )​? ​(c) What is Upper P (x overbar less than or equals 75.65 )​? ​(d) What is Upper P (79.4 less than x overbar less than 89.3 )​?
Mathematics
1 answer:
Ivanshal [37]3 years ago
8 0

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

You might be interested in
The sum of 6 and the product of 8 and x" into mathematical expression
Inga [223]

Answer:

6=8x

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Find the quotient of 18 and 120
DIA [1.3K]
Take 18 and divide it by 120. Your answer os 0.15
3 0
3 years ago
Read 2 more answers
Choose the function that the graph represents
gayaneshka [121]

Answer:

Where are the functions and the graph?

Step-by-step explanation:


6 0
3 years ago
Jack and Jill fetched 24 pints of water in their bucket. Jill drank a tenth of this, jack a quarter. They gave three eighths to
Minchanka [31]

Answer: See explanation

Step-by-step explanation:

Total water fetched = 24 pints.

Jill drank a tenth of this. This will be:

= 1/10 × 24

= 2.4 pints

Jack drank a quarter. This will be:

= 1/4 × 24 = 6.

They gave three eighths to dame Dob . Thus will be:

= 3/8 × 24

= 9

They gave a fifth to jill's mother. This will be:

= 1/5 × 24.

= 4.80

Amount that'll be left over will be:

= 24 - (2.40 + 6 + 9 + 4.80)

= 24 - 22.2

= 1.8

1.8 pints of water will be left over.

4 0
3 years ago
 Which of the following are solutions to the equation below?
Novosadov [1.4K]

Answer:

The answer to your question is F

6 0
2 years ago
Other questions:
  • Need quick math help please :\
    7·1 answer
  • the perimeters of the square and the equilateral triangle are equal. Which equation represents this scenario? What is the value
    12·2 answers
  • Please help with the following algebra question
    11·1 answer
  • What is the radius and diameter of the following circle?
    9·2 answers
  • If f(x) varies directly with x2, and f(x) = 40 when x = 2, find the value of f(5).
    6·1 answer
  • What the answer thanks
    6·1 answer
  • The length of the minute hand on a clock is 5 in....is it a dimeter, circumference, radius?
    5·1 answer
  • Solve the following equation:x^2=10
    15·2 answers
  • How is mathematical thinking established? How can we have mathematical thinking?<br><br> 修改翻译结果
    13·2 answers
  • Please answer this question, we have a test on it tomorrow. I will probably be posting more.... I will mark brainiest IF you get
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!