The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.
<h3>How to find the confidence interval?</h3>
To find the confidence interval C.I,
- Determine the mean(μ) of the sample
- Determine the standard deviation(σ)
- Determine the z-score for the given confidence level using the z-score table
- Using all these, the confidence interval is calculated by the formula, C. I = μ ± z(σ/√n) where n is the sample size and z(σ/√n) gives the margin error. So, we can also write C. I = mean ± margin error.
<h3>Calculation:</h3>
It is given that,
Sample size n = 225
Sample mean μ = 11.6
Standard deviation σ = 4.1
Since 95% confidence interval, z-score is 1.96
So, the required confidence interval is calculated by,
C. I = μ ± z(σ/√n) or mean ± margin error
On substituting,
C. I = 11.6 ± 1.96(4.1/√225)
= 11.6 ± 1.96 × 0.2733
= 11.6 ± 0.5357
So, the lower bound = 11.6 - 0.5357 = 11.065 and
the upper bound = 11.6 + 0.5357 = 12.135.
Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.
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Answer: 20
Step-by-step explanation:
Answer:
(2x-1)(2x+1)(x^2+2) = 0
Step-by-step explanation:
Here's a trick: Use a temporary substitution for x^2. Let p = x^2. Then 4x^4+7x^2-2=0 becomes 4p^2 + 7p - 2 = 0.
Find p using the quadratic formula: a = 4, b = 7 and c = -2. Then the discriminant is b^2-4ac, or (7)^2-4(4)(-2), or 49+32, or 81.
Then the roots are:
-7 plus or minus √81
p= --------------------------------
8
p = 2/8 = 1/4 and p = -16/8 = -2.
Recalling that p = x^2, we let p = x^2 = 1/4, finding that x = plus or minus 1/2. We cannot do quite the same thing with the factor p= -2 because the roots would be complex.
If x = 1/2 is a root, then 2x - 1 is a factor. If x = -1/2 is a root, then 2x+1 is a factor.
Let's multiply these two factors, (2x-1) and (2x+1), together, obtaining 4x^2 - 1. Let's divide this 4x^2 - 1 into 4x^4+7x^2-2=0. We get x^2+2 as quotient.
Then, 4x^4+7x^2-2=0 in factored form, is (2x-1)(2x+1)(x^2+2) = 0.
Answer: B
Step-by-step explanation:
you use the coordinates to find the sides
Answer:
no solution
Step-by-step explanation:
Given
(21 - 3a) = 6 - a ( multiply through by 3 to clear the fraction )
21 - 3a = 18 - 3a ( subtract 21 from both sides )
- 3a = - 3 - 3a ( add 3a to both sides )
0 = - 3 ← not possible
This indicates the equation has no solution
