Volume: The base of a pyramid is a rectangle with a length of 3 centimeters and a width of 6 centimeters. If the height of the p
1 answer:
You might be interested in
Answer:
c(p) = {0.2 p ⇒ p < 1000
0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000
0.29 p - 140 ⇒ p > 2000}
Step-by-step explanation:
* Lets explain how to solve the problem
- The profit is represented by p
1. If the profit is under $1,000, the commission rate is 20%
∵ The profit is p < 1000
∵ 20% of p = = 0.2 p
∵ c(p) is the function of the commission
∴ c(p) = 0.2 p when p < 1000
2. If the profit is at least $1,000 and less than or equal to $2,000, the
commission rate is 20% of the first $1,000 and 24% of the remainder
of the profit
- At least means greater than or equal
∵ The profit 1000 ≤ p ≤ 2000
- The commission is divided into 20% of first $1000 and 24% of
the reminder
∵ 20% of 1000 = = 200
∵ The remainder of the profit = p - 1000
∵ 24% of the remainder profit =
= 0.24(p - 1000) = 0.24 p - 240
∴ The total commission = 200 + 0.24 p - 240
∴ The total commission = 0.24 p - 40
∴ c(p) = 0.24 p - 40 when 1000 ≤ p ≤ 2000
3. If the profit is above $2,000, the rate is 20% of the first $1,000
of profit, 24% of the next $1,000 of profit, and 29% of the amount
of profit over $2,000
∵ The profit p > 2000
- The commission is divided into 20% of first $1000 and 24% of the
next $1,000 of profit, and 29% of the amount of profit over $2,000
∵ 20% of 1000 = = 200
∵ 24% of 1000 = = 240
- The amount of profit over $2,000 = p - 2000
∵ 29% of the amount of profit over $2,000 =
= 0.29(p - 2000)
= 0.29 p - 580
∴ The total commission = 200 + 240 + 0.29 p - 580
∴ The total commission = 0.29 p - 140
∴ c(p) = 0.29 p - 140 when p > 2000
* The commission function is:
c(p) = {0.2 p ⇒ p < 1000
0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000
0.29 p - 140 ⇒ p > 2000}
Answer:
The point estimate is 5,617.
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
The 98% confidence interval for the difference between the two population means is (5163, 6071).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Compound 1:
127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:
Compound 2:
163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:
Distribution of the difference:
The point estimate is 5,617.
Confidence interval
The confidence interval is:
In which
z is the z-score that has a p-value of .
The margin of error is:
98% confidence level
So , z is the value of Z that has a p-value of
, so
.
Margin of error:
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
For the confidence interval, as we round to the nearest whole number, we round it 454. So
The lower bound of the interval is:
The upper bound of the interval is:
The 98% confidence interval for the difference between the two population means is (5163, 6071).