Answer: 95% confidence interval = 20,000 ± 2.12
( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )
Step-by-step explanation:
Given :
Sample size(n) = 17
Sample mean = 20000
Sample standard deviation = 1,500
5% confidence
∴ = 0.025
Degree of freedom () = n-1 = 16
∵ Critical value at ( 0.025 , 16 ) = 2.12
∴ 95% confidence interval = mean ±
Critical value at 95% confidence interval = 20,000 ± 2.12
( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )
Hi, you've asked an incomplete question. Here are the remaining questions:
a) Describe what each region in the Venn diagram represents.
Region I: In drama club, not in step team.
Region II: In both clubs.
Region III: In step team not in drama.
Region IV: Not in either club.
b) How many students were in only one of the two clubs?
c) How many students were in the drama club or in the step team?
d) How many students were surveyed?
Attached is the Venn diagram depicting the regions.
Explanation:
b) By adding the number of students that like drama club and those that like step club we can derive the answer: 34 + 27 = 61.
c) By adding 34 + 27 + those that like both (14) = 75.
d) The total number of students surveyed is gotten by summing any number in attached the diagram: 34 + 27 + 14 + 13 = 88.
Answer:
So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the scores on the LSAT of a population, and for this case we know the distribution for X is given by:
Where and
We want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.35 of the area on the left and 0.65 of the area on the right it's z=-0.385. On this case P(Z<-0.385)=0.35 and P(Z>-0.385)=0.65
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.
