1. A car has a 16-gallon fuel tank. When driven on a highway, it has a gasmileage of 30 miles per gallon. The gas mileage (also
called "fuel efficiency")tells us the number of miles the car can travel for a particular amount of fuel(one gallon of gasoline, in this case). After filling the gas tank, the driver got ona highway and drove for a while.
1 answer:
Given:
Capacity of the car's fuel tank = 16 gallons
Gas mileage of car = 30 miles per gallon
Given that the driver filled the tank and got on a highway, let's solve for the following:
• (a) How many miles has the car traveled if it has the following amounts of gas left in the tank:
Use the expression:
Where g reresents the amount of gas left.
• 15 gallons:
If the car has 15 gallons left, to calculate the distance traveled, we have:
If the car has 15 gallons left, it has traveled for 30 miles.
• 10 gallons:
For 10 gallons, we have:
If the car has 10 gallons left, it has traveled for 180 miles.
• 2.5 gallons:
If the car has 2.5 gallons left, it has traveled for 405 miles.
• Part b.
Let's write an equation that shows the relationship between the distance traveled (d), and the amount of gas left in the tank in gallons(x).
To write the equation, we have:
• Part C.
Let's find the amount of gallons left in the tank when the car has traveled the following distances:
• 90 miles:
If the car has traveled 90 miles, it will have 13 gallons left in the tank.
• 246 miles:
If the car has traveled for 246 miles, it will have 7.8 gallons left in the tank.
• Part d.
To write the equation, we have:
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Answer:
Step-by-step explanation:
Hello!
For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.
In this example the variable is:
X: height of a college student. (cm)
There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.
The option you have is to apply the Central Limit Theorem.
The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.
As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.
The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:
X[bar]~~N(μ;σ2/n)
Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:
98% CI
1 - α: 0.98
⇒α: 0.02
α/2: 0.01
X[bar] ±
174.5 ±
[172.22; 176.78]
With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].
I hope it helps!