Does the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the tabl
1 answer:
The equation for the direct variation is y= kx (where k is contant of variation.)
This equation represent that if x will increase then y will also increase because it's k times x.
Where the equation for indirect variation is
By this equation if x will increase then y will decrease and vice versa.
The given data is :
x: 2 4 8 12
y: 4 2 1 2/3
Notice as x is increasing then y is decreasing. Like x has increased from 2 to 4 then y is decresing from 4 to 2 and so on.
So, the given data represent an indirect variation.
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Answer:
Step-by-step explanation:
The given probabilities are:
Their sum is
The probabilities that will complete the model should add up to so that the sum of all probabilities is 1.
Answer:
95.44% probability the resulting sample proportion is within .04 of the true proportion.
Step-by-step explanation:
To solve this question, 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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sampling distribution of the sample proportion in sample of size n, the mean is and the standard deviation is
In this question:
So
How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?
This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16.
X = 0.24
By the Central Limit Theorem
has a pvalue of 0.9772.
X = 0.16
has a pvalue of 0.0228.
0.9772 - 0.0228 = 0.9544
95.44% probability the resulting sample proportion is within .04 of the true proportion.