To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by 2, (b) find the critical value t Subscript alpha divided by 2, or (c) state that neither the normal nor the t distribution applies. 95%; nequals200; sigma equals 19.0; population appears to be skewe
Answers
Answer:
The correct option is (a).
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n > 30) from the population with replacement, then the distribution of the sample- means will be approximately normally-distributed.
Then, the mean of the sample means is given by,
And the standard deviation of the sample means is given by,
The information provided is:
n = 200
σ = 19.0
Population is skewed.
As the sample selected is quite large, i.e. n = 200 > 30 the central limit theorem can be used to approximate the distribution of the sample mean by the normal distribution.
So, .
Then to construct a confidence interval for mean we will use a z-interval.
And for 95% confidence level we will compute the critical value of z, i.e. .
Thus, the correct option is (a).
Related Questions
(c) In how many way we can list the digits{1,1,2,2,3,4,5}so that notwo identical digit are in consecutive positions?
Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?
The state department of transportation is coordinating road crews to fix potholes after a particularly snowy winter. Initial estimates gave an average of 7.8 potholes per mile of highway. Find the probability that there are 11 or more potholes in a randomly selected one-mile stretch of highway. Use Excel to find the probability.
A = 1 −7 −1 2 , B = 3 7 −1 0 , C = 1 0 −1 1 Find: a) BC, b) 5A − 2C, c) A + C,
Which point is a representation of cruising height in feet?
Point A
Point B
Point C
Point D
Answers
Answer:
Point C.
Step-by-step explanation:
Hope this helps!
Answer:
c
Step-by-step explanation:
hope i helped hehe :)
A. 2√3
OB. -12i
OC. -2√3
D. 2√31
E. 12/
Answers
Final answer:
The expression √√-12 is equivalent to -2√3.
Explanation:
The expression √√-12 represents the square root of the square root of -12. Since the square root of -12 is not a real number, the expression is not defined in the set of real numbers. However, it is possible to define the square root of a negative number using imaginary numbers. The choice equivalent to √√-12 is -2√3 or option C.
Learn more about Square roots and imaginary numbers here:
A. d=59
B. d=114
C. d=55
D. d=66
Answers
Answer:
A. d = 59°
Step-by-step explanation:
We know that the 3 angles added up together are a straight line or 180°. Therefore,
m∠d° = 180 - (57 + 64)
Answer: D. 59
Step-by-step explanation:
57 + 64 + d = 180°
121 + d = 180°
180 - 121 = 59°
Hope this helps!
Answers
Alisha needs tο use a fractiοn οf 3/8 οf each οf the ingredients οn the recipe.
What is Fractiοn?
A fractiοn is a way οf representing a part οf a whοle οr a ratiο between twο quantities. It is written in the fοrm οf a numeratοr and a denοminatοr separated by a hοrizοntal line οr slash (/), such as 3/4, where 3 is the numeratοr and 4 is the denοminatοr. The numeratοr represents the part being cοnsidered, and the denοminatοr represents the whοle οr the tοtal number οf equal parts.
The fractiοn οf each οne οf the οther ingredients that she needs tο use is equal tο the fractiοn between the number οf eggs that she has and the number οf eggs that the recipe calls, it is:
N = 3/8
Therefοre, Sο she needs tο use 3/8 οf each οf the ingredients that the recipe calls.
Learn more about fractions from given link:
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Answers
Answer:
4 emails per minute
Step-by-step explanation:
20/5=4
Answers
Answer and Step-by-step explanation:
Let x and y be two positive integers and their sum is 14:
X + y = 14
And the sum of square of this number is:
f = x2 + y2
= x2+ (14 – x)2
Differentiate with respect to x, we get:
F’(x) = [ x2 + (14 – x)2]’ = 0
2x + 2(14-x)(-1) = 0
2x +( 28 – 2x)(-1) = 0
2x – 28 +2x = 0
2x + 2x = 28
4x = 28
X = 7
Hence, y = 14 – x = 14 -7 = 7
Now taking second derivative test:
F”(x) > 0
For x = y = 7,f reaches its maximum value:
(7)2 + (7)2 = 49 + 49
= 98
F at endpoints x Є [ 0, 14]
F(0) = 02 + (14 – 0)2
= 196
F(14) = (14)2 + (14 – 14)2
= 196
Hence the sum of squares of these numbers is minimum when x = y = 7
And maximum when numbers are 0 and 14.
Final answer:
To find two positive integers such that their sum is 14, and the sum of their squares is minimized, we need to consider all possible pairs of positive integers and calculate their sums of squares. The pair (6, 8) has the minimum sum of squares of 100. To find two positive integers such that their sum is 14, and the sum of their squares is maximized, the pairs (1, 13) and (2, 12) both have the maximum sum of squares of 170. Since we need to find two positive integers, the pair (1, 13) is the answer.
Explanation:
To find two positive integers such that their sum is 14 and the sum of their squares is minimized, we need to consider all possible pairs of positive integers that add up to 14 and calculate their sums of squares. Let's list all the pairs:
- 1 and 13: 1^2 + 13^2 = 170
- 2 and 12: 2^2 + 12^2 = 148
- 3 and 11: 3^2 + 11^2 = 130
- 4 and 10: 4^2 + 10^2 = 116
- 5 and 9: 5^2 + 9^2 = 106
- 6 and 8: 6^2 + 8^2 = 100
- 7 and 7: 7^2 + 7^2 = 98
From the list, we can see that the pair (6, 8) has the minimum sum of squares, which is 100.
Similarly, to find two positive integers such that their sum is 14 and the sum of their squares is maximized, we need to again consider all possible pairs and calculate their sums of squares. Let's list the pairs:
- 1 and 13: 1^2 + 13^2 = 170
- 2 and 12: 2^2 + 12^2 = 148
- 3 and 11: 3^2 + 11^2 = 130
- 4 and 10: 4^2 + 10^2 = 116
- 5 and 9: 5^2 + 9^2 = 106
- 6 and 8: 6^2 + 8^2 = 100
- 7 and 7: 7^2 + 7^2 = 98
From the list, we can see that the pair (1, 13) and the pair (2, 12) both have the maximum sum of squares, which is 170. Since we need to find two positive integers, the pair (1, 13) is the answer.
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