Five submarines sink on the same day, and all five go down at the same spot where a sixth had previously sunk. How might they al
l lie at rest so that each submarine touches the other five? To simplify, arrange six wooden matches so that each match touches every other match. No bending or breaking allowed.
1 answer:
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Answer:
a) By the central limit theorem we know that if the random variable X="quantitative scores for young women", and we know that this distribution is normal.
And we are interested on the distribution for the sample mean , we know that distribution for the sample mean is given by:
And with that we have the assumptions required to apply the normal distribution to create the confidence interval since the distribution for is normal.
b)
c) We are confident (99%) that the true mean for the quantitative scores for young women is between (270.283;3279.717)
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=1077 represent the sample size
Part a
By the central limit theorem we know that if the random variable X="quantitative scores for young women", and we know that this distribution is normal.
And we are interested on the distribution for the sample mean , we know that distribution for the sample mean is given by:
And with that we have the assumptions required to apply the normal distribution to create the confidence interval since the distribution for is normal.
Part b
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.99 or 99%, 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(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (270.283;3279.717)
Part c
We are confident (99%) that the true mean for the quantitative scores for young women is between (270.283;3279.717)