Help with finding g(f(x)) f(x) = x squared - 3x + 2 g(x)= x+2
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Answer:
So on this case the 95% confidence interval would be given by (38.608;39.392)
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)
represent the population standard deviation
n=25 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
The margin of error is given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
And replacing we got:
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (38.608;39.392)
The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).
What is a normal distribution?
A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.
It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.
It is also known as probability distribution curve.
The normal distribution has two parameters:
- Mean
- Standard deviation
What is the shape of the normal distribution?
The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.
Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).
Know more about "normal distribution" here: brainly.com/question/15103234
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