Answer:
answer is in the picture.
SOLUTION:
Step 1 :
In this question, we are told that a marketing research company needs to estimate the average total compensation of CEOs in the service industry.
We also have that: Data were randomly collected from 38 CEOs and the 98% confidence interval was calculated to be ($2,181,260, $5,836,180).
Then, we are asked to find the margin error for the confidence interval.
Step 2:
We need to recall that:
![\text{Higher Confidence Interval, CI}_{H\text{ = }}X\text{ + }\frac{Z\sigma}{\sqrt[]{n}}](https://tex.z-dn.net/?f=%5Ctext%7BHigher%20Confidence%20Interval%2C%20CI%7D_%7BH%5Ctext%7B%20%3D%20%7D%7DX%5Ctext%7B%20%2B%20%7D%5Cfrac%7BZ%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%7D)
![\text{Lower Confidence Interval , CI}_{L\text{ }}=\text{ X - }\frac{Z\sigma}{\sqrt[]{n}}](https://tex.z-dn.net/?f=%5Ctext%7BLower%20Confidence%20Interval%20%2C%20CI%7D_%7BL%5Ctext%7B%20%7D%7D%3D%5Ctext%7B%20X%20-%20%7D%5Cfrac%7BZ%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%7D)
It means that:
![\text{Margin of error, }\frac{Z\sigma}{\sqrt[]{n}\text{ }}\text{ = }\frac{CI_{H\text{ - }}CI_L}{2}](https://tex.z-dn.net/?f=%5Ctext%7BMargin%20of%20error%2C%20%7D%5Cfrac%7BZ%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%5Ctext%7B%20%7D%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7BCI_%7BH%5Ctext%7B%20-%20%7D%7DCI_L%7D%7B2%7D)
where,
putting the values into the equation for the margin of error, we have that:
![\text{Margin of error,}\frac{Z\sigma}{\sqrt[]{n}\text{ }}\text{ = }\frac{5,836,180\text{ - }2,181,260\text{ }}{2}](https://tex.z-dn.net/?f=%5Ctext%7BMargin%20of%20error%2C%7D%5Cfrac%7BZ%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%5Ctext%7B%20%7D%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B5%2C836%2C180%5Ctext%7B%20%20-%20%7D2%2C181%2C260%5Ctext%7B%20%7D%7D%7B2%7D)
CONCLUSION:
The margin error for the confidence interval is 1, 827, 460
Given the simple interest formula:
I = P•R•T
where:
I = interest
P = principal
R = interest rate
T = time (in years)
We can isolate R algebraically to find out the interest rate:
I = P•R•T
Divide both sides by P•T:
I / (P•T) = (P•R•T)/(P•T)
The formula for the interest rate is:
R = I / (P•T)
Substitute the given values into this formula to solve for the interest rate (R):
R = I / (P•T)
R = $490/ ($1,400 • 5 years)
R = $490 / $7,000
R = 0.07 or 7%
Therefore, the interest rate is 7%.
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Answer:
Step-by-step explanation:
its 69 now answer ur phone tyvm
Answer: the probability that fewer than 100 in a random sample of 818 men are bald is 0.9830
Step-by-step explanation:
Given that;
p = 10% = 0.1
so let q = 1 - p = 1 - 0.1 = 0.9
n = 818
μ = np = 818 × 0.1 = 81.8
α = √(npq) = √( 818 × 0.1 × 0.9 ) = √73.62 = 8.58
Now to find P( x < 100)
we say;
Z = (X-μ / α) = ((100-81.8) / 8.58) = 18.2 / 8.58 = 2.12
P(x<100) = P(z < 2.12)
from z-score table
P(z < 2.12) = 0.9830
Therefore the probability that fewer than 100 in a random sample of 818 men are bald is 0.9830
