In a survey of 150 students at Kennedy Middle School, 48% said

If a random sample of size nequals=6 is taken from a population, what is required in order to say that the sampling distributio

goldenfox [79]

Answer:

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

In order to satisfy this distribution we need that each observation on this case comes from a normal distribution, because since the sample size is not large enough we can't apply the central limit theorem.

Step-by-step explanation:

For this case we have that the sample size is n =6

The sample man is defined as :

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And we want a normal distribution for the sample mean

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

In order to satisfy this distribution we need that each observation on this case comes from a normal distribution, because since the sample size is not large enough we can't apply the central limit theorem.

So for this case we need to satisfy the following condition:

$X_i \sim N(\mu , \sigma), i=1,2,...,n$

Because if we find the parameters we got:

$E(\bar X) =\frac{1}{n} \sum_{i=1}^n E(X_i) = \frac{n\mu}{n}=\mu$

$Var(\bar X)= \frac{1}{n^2} \sum_{i=1}^n Var(X_i) = \frac{n\sigma^2}{n^2}= \frac{\sigma^2}{n}$

And the deviation would be:

$Sd (\bar X) = \frac{\sigma}{\sqrt{n}}$

And we satisfy the condition:

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

3 0

2 years ago

An angle's supplement is nine times of its complementary angle. Find the measure of the angle, the complement of the angle,and t

Nezavi [6.7K]

S = 9C
first sentence written as an expression
Where S represents the angles supplement
and C represents the angles complement
A + S = 180
definition of supplementary allows me to make this statement Where A is the original angle
A + C = 90
definition of complimentary allows this statement
now add the prior 2 statements together
A + S + A + C = 180 + 90
now simplify
2A + S + C = 270
now replace S with 9C using first statement
2A + 9C + C = 270
now simplify
2A + 10C = 270
now divide both sides by 2
A + 5C = 135
now using the second statement isolate A by adding C to both sides
A = 90 - C
now combine the two prior statements
90 - C + 5C = 135
now simplify
90 + 4C = 135
now subtract 90 from both sides
4C = 45
now divide both sides by 4
C = 11.25
so the complimentary angle is 11.25
now take the third equation and substitute in C
A + 11.25 = 90
now subtract 11.25 from both sides
A = 78.75
so the original angle is 78.75
now use the second equation and substitute in A
78.75 + S = 180
now subtract 78.75 from both sides
S = 101.25
so the suplimentary angle is 101.25

7 0

3 years ago

Mr. Singh needed to understand the trend of his students’ latest test scores. Find the mean and median for each set of data, and

uranmaximum [27]

Answer:

See explanations below

Step-by-step explanation:

Mean is the average of the data

Mean = sum of data/sample size

Sum of data = 89+99+80+5+90+0+100+95

Sum of data = 558

Sample size = 8

Mean = 558/8

Mean = 69.75

Median is the data value in the middle after rearrangement

Rearrange

0 , 5, 80) 89, 90, (95, 99 100

Median = 89+90/2

Median = 89.5

The parameter that gives a better picture of the scores is the Mean since all the given datas are taken into consideration

5 0

3 years ago

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Use dimes, nickels, and pennies to show 42 cents. How many different ways can you show this amount?

Juli2301 [7.4K]

Answer:

U can use. Four dimes an two pennies

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Work out the area of a rectangle with base, <br>b<br>= 22mm and perimeter, <br>P<br>= 64mm.

Vsevolod [243]

Answer:220mm

Step-by-step explanation:

22x2=44

64-44=20

length =10mm

10mmx22mm=220mm

4 0

3 years ago

Read 2 more answers