what is the correct form of the partial fraction decomposition for: start fraction 35-27x over 4xsquared+28x endfraction
2 answers:
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Answer:
15.15% probability that the sample mean will be $192,000 or more.
Step-by-step explanation:
To solve this problem, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
The probability that the sample mean will be $192,000 or more is
This is 1 subtracted by the pvalue of z when X = 192000. So
By the Central Limit Theorem
has a pvalue of 0.8485.
1-0.8485 = 0.1515
15.15% probability that the sample mean will be $192,000 or more.
The volume of a cylinder is
Explanation:
Given that the diameter of the cylinder is 10 inches.
The radius of the cylinder is given by
Thus, the radius is 5 inches.
Also, given that the height is three times the radius.
Thus, we have,
Thus, the height is 15 inches.
The volume of the cylinder is given by
Substituting the values, we get,
Using the calculator, the value of pi is determined and multiplied with 375.
Hence, we have,
Thus, the volume of the cylinder is