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
At the skateboard park, the hot new attraction is the U-Dip, a cement structure embedded into the ground. The cross-sectional vi
Ratling [72]

Answer:

hahsbsaagvsaagags

Step-by-step explanation:

shahahavsvnwbwnsbhas

7 0
3 years ago
Help please the question is in the picture
scoundrel [369]

Answer: I know R2 is reflexive property.

Step-by-step explanation:

5 0
3 years ago
What is 1+2+3+4+5+6+7?
Elan Coil [88]

Answer:

28

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the product for 1/5 times 6/7
Vlad1618 [11]
6/35 is your answer answer answer sorry

5 0
3 years ago
What is a number that when you divide it by 4 and subtract 3 from the quotient, you get 13?
inysia [295]

64

//

64 \div 4 = 16

16 - 3 = 13

8 0
2 years ago
Read 2 more answers
Other questions:
  • What is b in 12-b=12.5
    5·1 answer
  • Write 63000 in standard form
    14·2 answers
  • Is 563 divisibly by 4
    13·2 answers
  • Expand:<br> 5 ( n - 1)??<br> could you please show working out to.<br> Thanks
    12·1 answer
  • I NEED HELP PLEASE!!!!!!!
    5·2 answers
  • Rapid Rental Car charges a $40 rental fee, $25 for gas, and $0.65 per mile driven. For the same car, Capital
    7·1 answer
  • What is $38.00 plus 80%?
    6·2 answers
  • En una nevería, si deseas consumir algún paquete de snacks tiene un costo de $30 y no te cobran la admisión. Si consideras x a l
    14·1 answer
  • In a circle of any size, what ratio does
    15·2 answers
  • The equations of three lines are given below.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!