A diver is 10 feet below the surface of the water and then descends 20 feet.what is the location of the diver after the descent?
2 answers:
You might be interested in
Answer:
And rounded up we have that n=385
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".
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 margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can use as an estimator for p . And replacing into equation (b) the values from part a we got:
And rounded up we have that n=385
Answer:
Ninety-five percent of consumers in the U.S. consumed less than 63.59 gallons.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
The standard deviation is the square root of the variance, so
Also, the mean is 42.2, so
Ninety-five percent of consumers in the U.S. consumed less than how many gallons?
The 95th percentile, which is the value of X when Z has a pvalue of 0.95. So X when
Ninety-five percent of consumers in the U.S. consumed less than 63.59 gallons.