If 6 numbers have a mean of 5, and five of the numbers are 3, 2, 1, 7, and 6, what is the sixth number?
1 answer:
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Answer:
Step-by-step explanation:
Hello!
The parameter of interest in this exercise is the population proportion of Asians that would welcome a person of other races in their family. Using the race of the welcomed one as categorizer we can define 3 variables:
X₁: Number of Asians that would welcome a white person into their families.
X₂: Number of Asians that would welcome a Latino person into their families.
X₃: Number of Asians that would welcome a black person into their families.
Now since we are working with the population that identifies as "Asians" the sample size will be: n= 251
Since the sample size is large enough (n≥30) you can apply the Central Limit Theorem and approximate the variable distribution to normal.
1. 95% CI for Asians that would welcome a white person.
If 79% would welcome a white person, then the expected value is:
E(X)= n*p= 251*0.79= 198.29
And the Standard deviation is:
V(X)= n*p*(1-p)= 251*0.79*0.21=41.6409
√V(X)= 6.45
You can construct the interval as:
E(X)±Z₁₋α/₂*√V(X)
198.29±1.965*6.45
[185.62;210.96]
With a 95% confidence level, you'd expect that the interval [185.62; 210.96] contains the number of Asian people that would welcome a White person in their family.
2. 95% CI for Asians that would welcome a Latino person.
If 71% would welcome a Latino person, then the expected value is:
E(X)= n*p= 251*0.71= 178.21
And the Standard deviation is:
V(X)= n*p*(1-p)= 251*0.71*0.29= 51.6809
√V(X)= 7.19
You can construct the interval as:
E(X)±Z₁₋α/₂*√V(X)
178.21±1.965*7.19
[164.08; 192.34]
With a 95% confidence level, you'd expect that the interval [164.08; 192.34] contains the number of Asian people that would welcome a Latino person in their family.
3. 95% CI for Asians that would welcome a Black person.
If 66% would welcome a Black person, then the expected value is:
E(X)= n*p= 251*0.66= 165.66
And the Standard deviation is:
V(X)= n*p*(1-p)= 251*0.66*0.34= 56.3244
√V(X)= 7.50
You can construct the interval as:
E(X)±Z₁₋α/₂*√V(X)
165.66±1.965*7.50
[150.92; 180.40]
With a 95% confidence level, you'd expect that the interval [150.92; 180.40] contains the number of Asian people that would welcome a Black person in their family.
I hope it helps!
Find sketch of parallelogram attached
Answer and explanation:
A parallelogram is a quadrilateral which is wider than it is long. A parallelogram has two sides parallel to the other. From the above, we are told the parallelogram PQRS has an angle QPS 120, with sides 10cm and 8cm, we use this to sketch the parallelogram
We find that angle QPS is 120 degrees hence angle RSP is 60 degrees since angle on straight line is 60 degrees from 180-120 in angle QPS and alternate angles are equal. Also opposite angles of a parallelogram are equal
Answer:
The third option (9+-
-
)
Step-by-step explanation:
With FOIL, this can be expanded. (a+b)(a-b) is equal to a²+ab-ab-b² or a²-b².
In this case, all the answers have 4 terms, so we want the first option. This makes the equation 3²+(3×)-(3×
)-(
)².
Solving these gives 9+-
-7. This is the same as 9+
-
-
.
**This content involves multiplying with surds and expanding perfect squares, which you may wish to revise. I'm always happy to help!