Answer:
The actual number of calories that Mya burned when she
trained for 30 minutes is 240.
Step-by-step explanation:
We have an exponential function that is the best fit for the number of calories Mya burns, in function of time (minutes).
The function is:
Where y: calories burned, and x: training time.
Whenever we use regression models, we have a real value and a predicted value. The difference between them, the measure we want to minimize when we adjust with this typo of models, is called residual.
In the table is shown as one of the columns.
For example, for x=10 minutes, we have a real value of 30 and a predicted value of 78.36, so the residual becomes e=30-78.36=-48.36.
For x=30 minutes, we have only the residual, that has a value of 5.53. That means that the predicted value, which we can calculate, is 5.53 below the real value.
The predicted value for x=30 is:
Using the equation for the residual e, we can calcualte the actual number of calories that Mya burned in 30 minutes:
The answer is:
The explanation is shown below:
1. Cynthia rounds the number, which is identified as , to one decimal place and the result is 6.3.
2. Based on this, we know that could have been between 6.25 and 6.35. Therefore, the error interval for
is given by:
Where indicates that the value 6.25 is included and
indicates that the value 6.35 is not included (Because if
had been exactly 6.35, Cynthia would round up to 6.4).
Answer:
So on this case the 95% confidence interval would be given by (12.150;16.690)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=36 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (12.150;16.690)
Answer: There are 60 ways that they can travel to the concert.
Step-by-step explanation:
Since we have given that
Number of people want to go to a concert = 12
Number of cars = 3
Number of drivers in the group = 5
So, using the "Fundamental theorem of counting":
We get that
Hence, there are 60 ways that they can travel to the concert.
