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
Wittaler [7]
3 years ago
13

A simple random sample of size equals 49 is obtained from a population with mu equals 84 and sigma equals 14. ​(a) Describe the

sampling distribution of x overbar. ​(b) What is Upper P (x overbar greater than 87.8 )​
Mathematics
1 answer:
Gelneren [198K]3 years ago
5 0

Answer:

(a) The sampling distribution of \bar X is given by;

             \bar X ~ Normal (\mu =84, s = \frac{\sigma}{\sqrt{n} } =\frac{14}{\sqrt{49} } )

(b) P(\bar X > 87.8) = 0.0287

Step-by-step explanation:

We are given that a simple random sample of size equals 49 is obtained from a population with mu equals 84 and sigma equals 14.

<em><u>Let </u></em>\bar X<em><u> = sample mean</u></em>

The z-score probability distribution for sample mean is given by;

                             Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean = 84

            \sigma = standard deviation = 14

            n = sample size = 49

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

(a) The sampling distribution of \bar X is given by;

             \bar X ~ Normal (\mu =84, s = \frac{\sigma}{\sqrt{n} } =\frac{14}{\sqrt{49} } )

(b) Probability of \bar X greater than 87.8 is given by = P(\bar X > 87.8)

     

      P(\bar X > 87.8) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{87.8-84}{\frac{14}{\sqrt{49} } } ) = P(Z > 1.90) = 1 - P(Z \leq 1.90)

                                                        = 1 - 0.9713 = <u>0.0287</u>

The above probability is calculated by looking at the value of x = 1.90 in the z table which has an area of 0.9713.

You might be interested in
A video game maker claims that number of glitches in code for their
svet-max [94.6K]

Answer:

The major condition that needs to be satisfied before a t-test is performed that the question satisfies easily is the use of random sampling to obtain sample data.

Step-by-step explanation:

The major conditions necessary to conduct a t-test about a mean include;

- The sample extracted from the population must be extracted using random sampling. That is, the sample must be a random sample of the population.

- The sampling distribution must be normal or approximately normal. This is achievable when the population distribution is normal or approximately normal.

- Each observation in the sample data must have an independent outcome. That is, the outcome/result of each sub-data mustn't depend on one another.

Of the three conditions that need to be satisfied before the conduction of a t-test, the first condition about using a random sampling technique is evidently satisfied.

It is stated in the question that 'A private investigator hired by a competitor takes a random sample of 47 games and tries to determine if there are more than 7 glitches per game'.

Hope this Helps!!!

5 0
3 years ago
The differnce between 3 and 11
Lynna [10]

Answer:

-8

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
At Open Skate Night, admission is $3.50 with a membership card and $4.00 without a membership card. Skate rentals are $2.00.
zaharov [31]

Answer:

                                   

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Find the value of x in each pair of similar figures​
LekaFEV [45]

Answer:

8

Step-by-step explanation:

the pair of triangles is showing a dilations with a scale factor of 2

6/3=2

so it gives us 4 as the before answer and 4x2=8 so x=8

5 0
2 years ago
Read 2 more answers
PLEASE HELP!!! WILL MARK BRAINLIEST!!! CAN you help there is a website it has the answers appealy but I cannot seem to find them
miv72 [106K]

Answer:

The difference is While pay grades are administrative classifications used primarily to standardize compensation across the military services, ranks indicate a level of responsibility (for personnel, equipment, and mission) which grows with each increase in rank.      

Step-by-step explanation:

There similar because Pay grades E-1 through E-3 generally indicate basic training, advanced training or entry-level work. For the Army and Marines, E-1 corresponds to the rank of private

I hoped this helped!

3 0
2 years ago
Other questions:
  • ????????????????????
    6·1 answer
  • HELP GUYS IM GONNA FAIL MY CLASS HELPPPPPPPPPPPPPP
    9·2 answers
  • In the figure below, m /1 (x-97 and m.2 -<br>Find the angle measures.
    7·1 answer
  • What is the product?
    9·2 answers
  • Can someone please help me
    5·1 answer
  • What is 32% of 60? (Show work)
    14·1 answer
  • In science, students are observing the growth of two plants. Plant A recieves sunlight and Plant B does not. The graph and table
    13·2 answers
  • Question 4
    6·1 answer
  • Riley goes to a store an buys an item that costs x dollars. She has a coupon for 10% off, and then a 8% tax is added to the disc
    6·2 answers
  • Determine the domain of the following graph:
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!