Suzanne bought a sweater at the sale price of $29.99. the original cost of the seater was $49.99. what percent represents the di
2 answers:
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Answer:
So on this case the 95% confidence interval would be given by (5.56;6.96)
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 for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Assuming a Confidence of 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: "=-T.INV(0.025,49)".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 (5.56;6.96)
Answer:
the tank can hold 12.5 gallons when it is full
Step-by-step explanation:
Let's assume
tank can hold 'x' gallons when it is full
we are given
The gas gauge in a car shows it has 40% of a tank of gas
So, gas in car is
and we have
the car has about 5 gallons
so, we can set it equal
and then we can solve for x
Multiply both sides 5
we get
So, the tank can hold 12.5 gallons when it is full