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Answer:
And that represent the proportion of failures.
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 99% confidence interval would be given by (0.0475;0.2185)
Step-by-step explanation:
Previous concept
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".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The proportion estimated would be:
And that represent the proportion of failures.
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 99% confidence interval would be given by (0.0475;0.2185)
The average value of a data set is equal to the sum of each entry divided by the number of entries. In this case, we have 5 scores, so we can find set up the following equation where x is the fifth score:
Now solve for x:
The fifth score must be 87.
Now solve for x:
The fifth score must be 87.
bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.
le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.